- published: 13 Jul 2023
- views: 58
JSJ decomposition
In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem:
The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson. The first two worked together, and the third worked independently.
The characteristic submanifold
An alternative version of the JSJ decomposition states:
The submanifold Σ with the smallest number of boundary tori is called the characteristic submanifold of M; it is unique (up to isotopy).
The boundary of the characteristic submanifold Σ is a union of tori that are almost the same as the tori appearing in the JSJ decomposition. However there is a subtle difference: if one of the tori in the JSJ decomposition is "non-separating", then the boundary of the characteristic submanifold has two parallel copies of it (and the region between them is a Seifert manifold isomorphic to the product of a torus and a unit interval). The set of tori bounding the characteristic submanifold can be characterised as the unique (up to isotopy) minimal collection of disjointly embedded incompressible tori such that closure of each component of the 3-manifold obtained by cutting along the tori is either atoroidal or Seifert-fibered.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/JSJ_decomposition
Podcasts:
JSJ
ALBUMS
- Ministry of Sound: The Annual Spring 2002 released: 2002
- Chillout Classics: The Ultimate Chillout Collection released: 2002
- Renaissance Ibiza 2001 released: 2001
- Interpretations II released: 2001
- Renaissance Anthems 2002 released: 2001
- Spundae Presents: Interpretations II - Jerry Bonham released:
- Interpretations II released:
- Ibiza by Night released:
Ministry of Sound: The Annual Spring 2002
Released 2002- Point of View
- So Lonely
- Where's Your Head At
- It's Love (Trippin')
- Love Will Set You Free (Jambe Myth)
- At Night
- Young Hearts
- Nothing 2 Prove
- Gotta Get Thru This (Stella Browne vocal mix)
- Trippin (Agent Sumo's mix)
- Music Makes Me Happy (extended mix)
- Sunglasses at Night
- Glitterball
- La La Land
- New Dawn
- The Trick
- Alfies Groove
- Want Me
- God's Child (BBT club mix)
Renaissance Ibiza 2001
Released 2001- Another Chance (original mix)
- Babarabatiri (Tee's Latin mix)
- Happy People (Chocolate Puma remix)
- Promised Land (Max Linen mix)
- Yanu (original mix)
- Ride the Rhythm (Joey Negro club mix)
- The Sun (Tee's Sound Design mix)
- The Talk
- Night @ the Black (main mix)
- 24 Hours
- Come Home (Agent Sumo's Lil Devious remix)
- Drop Some Drums (original version)
- Turn It Up (Angelstereomix)
- Jetfunk (original version)
- Never Enough (Chocolate Puma remix)
Renaissance Anthems 2002
Released 2001- My Friend (Dorfmeister vs. Madrid de los Austrias dub)
- Eple
- Crazy Baby (Groove Armada mix)
- Summer in the Studio (radio edit)
- Guitarra G (Afterlife mix)
- Sunset (KV5 remix)
- Happy People (Christian J Rhodes Island remix)
- Hear My Soul
- Come Home (Carpel Tunnel Vision remix)
- Breathe (Flatline's Ambient Weekender)
- Lovely Head
- After Hours
- Playing to Win (Vocal version)
- Light a Rainbow (Almadrava remix)
- Glowing Yellow
- Deep Love 9 (Ambient mix)
Jon St. John
ALBUMS
-
Zlil Sela: Automorphisms of groups and a higher rank JSJ decomposition
Atelier sur Groupes autour de 3-variétés/ Workshop on Groups around 3-Manifolds (Juin/June 05-16 2023) Juin/June 12 : Webpage : https://www.crmath.ca/en/activities/#/type/activity/id/3857 Program: https://crm.umontreal.ca/2023/3Manifolds/pdf/schedule-Manifolds-w2.pdf The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. We generalize the structure and the construction of the JSJ decomposition, to study the automorphisms of a (colorable) hierarchically hyperbolic group that satisfies some weak acylindricity conditions. The object that we construct can be viewed as a higher rank JSJ decomposition. Like the JSJ decomposition of a hyperbolic group ...
published: 13 Jul 2023 -
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups. Later, the JSJ was generalized to all finitely presented groups. In this generality it encodes the splittings but not all the automorphisms. We further generalize the JSJ decomposition to study automorphisms of groups that act on products of hyperbolic spaces, and more generally to study automorphisms of (some) hierarchically hyperbolic groups (e.g. right angled Artin groups). The object that we construct can be viewed as a higher rank JSJ decomposition.
published: 06 Sep 2021 -
NCNGT2020: Volume Conjecture, geometric decomposition and deformation of hyperbolic structures (II)
Hi everyone! This to the second and the last talk of the series "Volume Conjecture, geometric decomposition and deformation of hyperbolic structures". Last time, we discussed how the asymptotics of the quantum invariants for hyperbolic links and 3-manifolds are related to 3 dimensional hyperbolic geometry. This time, we will focus on some satellite links whose complements have more than one hyperbolic piece in the geometric decomposition, and relate the asymptotics of their colored Jones polynomials to the geometric structures on the geometric pieces. Preprints are available on arxiv: - Asymptotics of some quantum invariants of the Whitehead chains, https://arxiv.org/abs/1912.10638 - Volume conjecture, geometric decomposition and deformation of hyperbolic structures https://arxiv.org/ab...
published: 24 May 2020 -
Benjamin Barrett: Gromov boundaries and Bowditch's JSJ decomposition
It is a fundamental principle in geometric group theory that large scale geometric properties of metric spaces on which a group acts should be considered properties of the group itself. If a given group acts on a hyperbolic metric space, then a particularly natural example of such a large-scale property is the Gromov boundary of that space: this is a topological space that compactifies the hyperbolic space at infinity. Connectivity properties of this boundary tell us how we can cut the group up into simpler pieces: a famous theorem of Stallings says that the group splits (as an amalgamated product or HNN extension) over a finite group if and only if the boundary is disconnected. In fact, one can say more: work of Brian Bowditch tells us that the structure of the collection of local cut poi...
published: 02 Apr 2021 -
Complexities of 3-manifolds
Knots and Spatial Graphs 2015 Complexities of 3-manifolds/ Jae Choon Cha (POSTECH)/ 2015-11-06
published: 24 May 2017 -
Symplectic fillings of lens spaces / Austin Christian / NCNGT 2021
Using the JSJ decomposition for symplectic fillings developed in our first talk, we complete the classification (up to diffeomorphism) of exact symplectic fillings of lens spaces. This is joint work with Youlin Li, and our result was independently obtained by John Etnyre and Agniva Roy. This is the second of a pair of talks presented at NCNGT 2021. Here's the first: https://youtu.be/OQLa-E1bXCM
published: 07 Jun 2021 -
Martin Bobb: Decomposition along flats for convex projective manifolds
Real convex projective geometry generalizes hyperbolic geometry in a way that allows for interesting deformation theory and also aspects of non-positive curvature. In this talk I will introduce convex projective geometry, and we will discuss a natural decomposition of compact convex projective manifolds along their codimension-1 flat substructures. This extends a celebrated 2006 result of Benoist: a 'geometric JSJ-decomposition' for compact convex projective 3-manifolds to manifolds of every dimension (greater than 2).
published: 26 Jun 2020 -
"Conformal dimension and decompositions of hyperbolic groups," John Mackay, NYGT, 10/22/2021
"Conformal dimension and decompositions of hyperbolic groups," John Mackay (University of Bristol), New York Group Theory Seminar, 10/22/2021
published: 22 Oct 2021 -
Geometry of complex surface singularities and 3-manifolds - Neumann
Geometric Structures on 3-manifolds Topic: Geometry of complex surface singularities and 3-manifolds Speaker: Walter Neumann Date: Tuesday, January 26 I will talk about bilipschitz geometry of complex algebraic sets, focusing on the local geometry in dimension 2 (complex surface singularities), where the topological classification has long been understood in terms of 3-manifolds, while the analytic classification, even in this low dimension, is still very much out of reach. Bilipschitz geometry lies between the extremes of topological and analytic type. Although it leads to a "tame" classification (as first conjectured by Siebenmann and Sullivan in the 70's and proved by Mostowski in the mid-eighties), it is only in the last decade that the richness of the bilipschitz classification has b...
published: 26 Jan 2016 -
"Geometric Topology of 3-manifolds" by Prof. Krüger Ramos Álvaro (Part.2/4)
Abstract: One of the greatest achievements on mathematics in the 21st century is the proof of the Poincaré's Conjecture by Grigory Perelman in 2003. Indeed, Perelman proved a much stronger result, which is the Geometrization Conjecture proposed by William Thurston in 1982. In order to do so, Perelman used the Ricci flow, a geometric/analytical argument proposed by Richard Hamilton. In this course, thought for a student with some background in Riemannian geometry, we will present Poincaré's conjecture in the context of the geometrization, explain the Geometrization theorem together with the eight Thurston's geometries and give an intuitive overview of the proof of Perelman. ☝️ Krüger Ramos Álvaro is professor at Universidade Federal do Rio Grande do Sul, Brazil. This course was filmed at ...
published: 08 Dec 2022
52:35
Zlil Sela: Automorphisms of groups and a higher rank JSJ decomposition
- Order: Reorder
- Duration: 52:35
- Uploaded Date: 13 Jul 2023
- views: 58
Atelier sur Groupes autour de 3-variétés/ Workshop on Groups around 3-Manifolds (Juin/June 05-16 2023)
Juin/June 12 :
Webpage : https://www.crmath.ca/en/activi...
Atelier sur Groupes autour de 3-variétés/ Workshop on Groups around 3-Manifolds (Juin/June 05-16 2023)
Juin/June 12 :
Webpage : https://www.crmath.ca/en/activities/#/type/activity/id/3857
Program: https://crm.umontreal.ca/2023/3Manifolds/pdf/schedule-Manifolds-w2.pdf
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. We generalize the structure and the construction of the JSJ decomposition, to study the automorphisms of a (colorable) hierarchically hyperbolic group that satisfies some weak acylindricity conditions. The object that we construct can be viewed as a higher rank JSJ decomposition. Like the JSJ decomposition of a hyperbolic group it encodes information on the algebraic structure of the automorphism group and on the dynamics of individual automorphisms.
https://wn.com/Zlil_Sela_Automorphisms_Of_Groups_And_A_Higher_Rank_Jsj_Decomposition
Atelier sur Groupes autour de 3-variétés/ Workshop on Groups around 3-Manifolds (Juin/June 05-16 2023)
Juin/June 12 :
Webpage : https://www.crmath.ca/en/activities/#/type/activity/id/3857
Program: https://crm.umontreal.ca/2023/3Manifolds/pdf/schedule-Manifolds-w2.pdf
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. We generalize the structure and the construction of the JSJ decomposition, to study the automorphisms of a (colorable) hierarchically hyperbolic group that satisfies some weak acylindricity conditions. The object that we construct can be viewed as a higher rank JSJ decomposition. Like the JSJ decomposition of a hyperbolic group it encodes information on the algebraic structure of the automorphism group and on the dynamics of individual automorphisms.
58:42
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
- Order: Reorder
- Duration: 58:42
- Uploaded Date: 06 Sep 2021
- views: 713
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theo...
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups.
Later, the JSJ was generalized to all finitely presented groups. In this generality it encodes the splittings but not all the automorphisms.
We further generalize the JSJ decomposition to study automorphisms of groups that act on products of hyperbolic spaces, and more generally to study automorphisms of (some) hierarchically hyperbolic groups (e.g. right angled Artin groups). The object that we construct can be viewed as a higher rank JSJ decomposition.
https://wn.com/Zlil_Sela_Automorphisms_Of_Groups_And_A_Higher_Rank_Jsj_Decomposition
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups.
Later, the JSJ was generalized to all finitely presented groups. In this generality it encodes the splittings but not all the automorphisms.
We further generalize the JSJ decomposition to study automorphisms of groups that act on products of hyperbolic spaces, and more generally to study automorphisms of (some) hierarchically hyperbolic groups (e.g. right angled Artin groups). The object that we construct can be viewed as a higher rank JSJ decomposition.
- published: 06 Sep 2021
- views: 713
24:53
NCNGT2020: Volume Conjecture, geometric decomposition and deformation of hyperbolic structures (II)
- Order: Reorder
- Duration: 24:53
- Uploaded Date: 24 May 2020
- views: 88
Hi everyone! This to the second and the last talk of the series "Volume Conjecture, geometric decomposition and deformation of hyperbolic structures".
Last tim...
Hi everyone! This to the second and the last talk of the series "Volume Conjecture, geometric decomposition and deformation of hyperbolic structures".
Last time, we discussed how the asymptotics of the quantum invariants for hyperbolic links and 3-manifolds are related to 3 dimensional hyperbolic geometry. This time, we will focus on some satellite links whose complements have more than one hyperbolic piece in the geometric decomposition, and relate the asymptotics of their colored Jones polynomials to the geometric structures on the geometric pieces.
Preprints are available on arxiv:
- Asymptotics of some quantum invariants of the Whitehead chains,
https://arxiv.org/abs/1912.10638
- Volume conjecture, geometric decomposition and deformation of hyperbolic structures
https://arxiv.org/abs/1912.11779
https://wn.com/Ncngt2020_Volume_Conjecture,_Geometric_Decomposition_And_Deformation_Of_Hyperbolic_Structures_(Ii)
Hi everyone! This to the second and the last talk of the series "Volume Conjecture, geometric decomposition and deformation of hyperbolic structures".
Last time, we discussed how the asymptotics of the quantum invariants for hyperbolic links and 3-manifolds are related to 3 dimensional hyperbolic geometry. This time, we will focus on some satellite links whose complements have more than one hyperbolic piece in the geometric decomposition, and relate the asymptotics of their colored Jones polynomials to the geometric structures on the geometric pieces.
Preprints are available on arxiv:
- Asymptotics of some quantum invariants of the Whitehead chains,
https://arxiv.org/abs/1912.10638
- Volume conjecture, geometric decomposition and deformation of hyperbolic structures
https://arxiv.org/abs/1912.11779
- published: 24 May 2020
- views: 88
1:04:39
Benjamin Barrett: Gromov boundaries and Bowditch's JSJ decomposition
- Order: Reorder
- Duration: 1:04:39
- Uploaded Date: 02 Apr 2021
- views: 222
It is a fundamental principle in geometric group theory that large scale geometric properties of metric spaces on which a group acts should be considered proper...
It is a fundamental principle in geometric group theory that large scale geometric properties of metric spaces on which a group acts should be considered properties of the group itself. If a given group acts on a hyperbolic metric space, then a particularly natural example of such a large-scale property is the Gromov boundary of that space: this is a topological space that compactifies the hyperbolic space at infinity. Connectivity properties of this boundary tell us how we can cut the group up into simpler pieces: a famous theorem of Stallings says that the group splits (as an amalgamated product or HNN extension) over a finite group if and only if the boundary is disconnected. In fact, one can say more: work of Brian Bowditch tells us that the structure of the collection of local cut points in the boundary determines a canonical JSJ decomposition for the group. In this talk I'll describe how Bowditch's JSJ decomposition is built from the structure of the boundary.
https://wn.com/Benjamin_Barrett_Gromov_Boundaries_And_Bowditch's_Jsj_Decomposition
It is a fundamental principle in geometric group theory that large scale geometric properties of metric spaces on which a group acts should be considered properties of the group itself. If a given group acts on a hyperbolic metric space, then a particularly natural example of such a large-scale property is the Gromov boundary of that space: this is a topological space that compactifies the hyperbolic space at infinity. Connectivity properties of this boundary tell us how we can cut the group up into simpler pieces: a famous theorem of Stallings says that the group splits (as an amalgamated product or HNN extension) over a finite group if and only if the boundary is disconnected. In fact, one can say more: work of Brian Bowditch tells us that the structure of the collection of local cut points in the boundary determines a canonical JSJ decomposition for the group. In this talk I'll describe how Bowditch's JSJ decomposition is built from the structure of the boundary.
- published: 02 Apr 2021
- views: 222
47:44
Complexities of 3-manifolds
- Order: Reorder
- Duration: 47:44
- Uploaded Date: 24 May 2017
- views: 159
Knots and Spatial Graphs 2015
Complexities of 3-manifolds/ Jae Choon Cha (POSTECH)/ 2015-11-06
Knots and Spatial Graphs 2015
Complexities of 3-manifolds/ Jae Choon Cha (POSTECH)/ 2015-11-06
https://wn.com/Complexities_Of_3_Manifolds
Knots and Spatial Graphs 2015
Complexities of 3-manifolds/ Jae Choon Cha (POSTECH)/ 2015-11-06
- published: 24 May 2017
- views: 159
25:25
Symplectic fillings of lens spaces / Austin Christian / NCNGT 2021
- Order: Reorder
- Duration: 25:25
- Uploaded Date: 07 Jun 2021
- views: 29
Using the JSJ decomposition for symplectic fillings developed in our first talk, we complete the classification (up to diffeomorphism) of exact symplectic filli...
Using the JSJ decomposition for symplectic fillings developed in our first talk, we complete the classification (up to diffeomorphism) of exact symplectic fillings of lens spaces. This is joint work with Youlin Li, and our result was independently obtained by John Etnyre and Agniva Roy.
This is the second of a pair of talks presented at NCNGT 2021. Here's the first: https://youtu.be/OQLa-E1bXCM
https://wn.com/Symplectic_Fillings_Of_Lens_Spaces_Austin_Christian_Ncngt_2021
Using the JSJ decomposition for symplectic fillings developed in our first talk, we complete the classification (up to diffeomorphism) of exact symplectic fillings of lens spaces. This is joint work with Youlin Li, and our result was independently obtained by John Etnyre and Agniva Roy.
This is the second of a pair of talks presented at NCNGT 2021. Here's the first: https://youtu.be/OQLa-E1bXCM
- published: 07 Jun 2021
- views: 29
49:21
Martin Bobb: Decomposition along flats for convex projective manifolds
- Order: Reorder
- Duration: 49:21
- Uploaded Date: 26 Jun 2020
- views: 50
Real convex projective geometry generalizes hyperbolic geometry in a way that allows for interesting deformation theory and also aspects of non-positive curvatu...
Real convex projective geometry generalizes hyperbolic geometry in a way that allows for interesting deformation theory and also aspects of non-positive curvature. In this talk I will introduce convex projective geometry, and we will discuss a natural decomposition of compact convex projective manifolds along their codimension-1 flat substructures. This extends a celebrated 2006 result of Benoist: a 'geometric JSJ-decomposition' for compact convex projective 3-manifolds to manifolds of every dimension (greater than 2).
https://wn.com/Martin_Bobb_Decomposition_Along_Flats_For_Convex_Projective_Manifolds
Real convex projective geometry generalizes hyperbolic geometry in a way that allows for interesting deformation theory and also aspects of non-positive curvature. In this talk I will introduce convex projective geometry, and we will discuss a natural decomposition of compact convex projective manifolds along their codimension-1 flat substructures. This extends a celebrated 2006 result of Benoist: a 'geometric JSJ-decomposition' for compact convex projective 3-manifolds to manifolds of every dimension (greater than 2).
- published: 26 Jun 2020
- views: 50
1:04:05
"Conformal dimension and decompositions of hyperbolic groups," John Mackay, NYGT, 10/22/2021
- Order: Reorder
- Duration: 1:04:05
- Uploaded Date: 22 Oct 2021
- views: 170
"Conformal dimension and decompositions of hyperbolic groups," John Mackay (University of Bristol), New York Group Theory Seminar, 10/22/2021
"Conformal dimension and decompositions of hyperbolic groups," John Mackay (University of Bristol), New York Group Theory Seminar, 10/22/2021
https://wn.com/Conformal_Dimension_And_Decompositions_Of_Hyperbolic_Groups,_John_Mackay,_Nygt,_10_22_2021
"Conformal dimension and decompositions of hyperbolic groups," John Mackay (University of Bristol), New York Group Theory Seminar, 10/22/2021
- published: 22 Oct 2021
- views: 170
58:45
Geometry of complex surface singularities and 3-manifolds - Neumann
- Order: Reorder
- Duration: 58:45
- Uploaded Date: 26 Jan 2016
- views: 2042
Geometric Structures on 3-manifolds
Topic: Geometry of complex surface singularities and 3-manifolds
Speaker: Walter Neumann
Date: Tuesday, January 26
I will t...
Geometric Structures on 3-manifolds
Topic: Geometry of complex surface singularities and 3-manifolds
Speaker: Walter Neumann
Date: Tuesday, January 26
I will talk about bilipschitz geometry of complex algebraic sets, focusing on the local geometry in dimension 2 (complex surface singularities), where the topological classification has long been understood in terms of 3-manifolds, while the analytic classification, even in this low dimension, is still very much out of reach. Bilipschitz geometry lies between the extremes of topological and analytic type. Although it leads to a "tame" classification (as first conjectured by Siebenmann and Sullivan in the 70's and proved by Mostowski in the mid-eighties), it is only in the last decade that the richness of the bilipschitz classification has become evident. I will describe work of Lev Birbrair, Anne Pichon and myself, on bilipschitz classification of complex surface germs in terms of refined JSJ decomposition of their 3-manifold links plus associated rational invariants, and if time permits, also the relationship of the classification with Zariski equisingularity, which was Zariski's approach to a tame classification.
For more videos visit http;//video.ias.edu
https://wn.com/Geometry_Of_Complex_Surface_Singularities_And_3_Manifolds_Neumann
Geometric Structures on 3-manifolds
Topic: Geometry of complex surface singularities and 3-manifolds
Speaker: Walter Neumann
Date: Tuesday, January 26
I will talk about bilipschitz geometry of complex algebraic sets, focusing on the local geometry in dimension 2 (complex surface singularities), where the topological classification has long been understood in terms of 3-manifolds, while the analytic classification, even in this low dimension, is still very much out of reach. Bilipschitz geometry lies between the extremes of topological and analytic type. Although it leads to a "tame" classification (as first conjectured by Siebenmann and Sullivan in the 70's and proved by Mostowski in the mid-eighties), it is only in the last decade that the richness of the bilipschitz classification has become evident. I will describe work of Lev Birbrair, Anne Pichon and myself, on bilipschitz classification of complex surface germs in terms of refined JSJ decomposition of their 3-manifold links plus associated rational invariants, and if time permits, also the relationship of the classification with Zariski equisingularity, which was Zariski's approach to a tame classification.
For more videos visit http;//video.ias.edu
- published: 26 Jan 2016
- views: 2042
1:38:59
"Geometric Topology of 3-manifolds" by Prof. Krüger Ramos Álvaro (Part.2/4)
- Order: Reorder
- Duration: 1:38:59
- Uploaded Date: 08 Dec 2022
- views: 58
Abstract: One of the greatest achievements on mathematics in the 21st century is the proof of the Poincaré's Conjecture by Grigory Perelman in 2003. Indeed, Pe...
Abstract: One of the greatest achievements on mathematics in the 21st century is the proof of the Poincaré's Conjecture by Grigory Perelman in 2003. Indeed, Perelman proved a much stronger result, which is the Geometrization Conjecture proposed by William Thurston in 1982. In order to do so, Perelman used the Ricci flow, a geometric/analytical argument proposed by Richard Hamilton. In this course, thought for a student with some background in Riemannian geometry, we will present Poincaré's conjecture in the context of the geometrization, explain the Geometrization theorem together with the eight Thurston's geometries and give an intuitive overview of the proof of Perelman.
☝️ Krüger Ramos Álvaro is professor at Universidade Federal do Rio Grande do Sul, Brazil.
This course was filmed at ICTP (Trieste, Italy) from October 24 to 27, 2022.
------------------------------------------------
Follow CIMPA news:
Website: https://www.cimpa.info
Facebook: https://bit.ly/3sY8OdQ
Twitter: https://twitter.com/cimpa_math
LinkedIn: https:https://bit.ly/3rHfrRs
https://wn.com/Geometric_Topology_Of_3_Manifolds_By_Prof._Krüger_Ramos_Álvaro_(Part.2_4)
Abstract: One of the greatest achievements on mathematics in the 21st century is the proof of the Poincaré's Conjecture by Grigory Perelman in 2003. Indeed, Perelman proved a much stronger result, which is the Geometrization Conjecture proposed by William Thurston in 1982. In order to do so, Perelman used the Ricci flow, a geometric/analytical argument proposed by Richard Hamilton. In this course, thought for a student with some background in Riemannian geometry, we will present Poincaré's conjecture in the context of the geometrization, explain the Geometrization theorem together with the eight Thurston's geometries and give an intuitive overview of the proof of Perelman.
☝️ Krüger Ramos Álvaro is professor at Universidade Federal do Rio Grande do Sul, Brazil.
This course was filmed at ICTP (Trieste, Italy) from October 24 to 27, 2022.
------------------------------------------------
Follow CIMPA news:
Website: https://www.cimpa.info
Facebook: https://bit.ly/3sY8OdQ
Twitter: https://twitter.com/cimpa_math
LinkedIn: https:https://bit.ly/3rHfrRs
- published: 08 Dec 2022
- views: 58
PLAYLIST TIME:
PLAYLIST TIME:
52:35
Zlil Sela: Automorphisms of groups and a higher rank JSJ decomposition
Atelier sur Groupes autour de 3-variétés/ Workshop on Groups around 3-Manifolds (Juin/June...
published: 13 Jul 2023
Zlil Sela: Automorphisms of groups and a higher rank JSJ decomposition
Zlil Sela: Automorphisms of groups and a higher rank JSJ decomposition
- Report rights infringement
- published: 13 Jul 2023
- views: 58
Atelier sur Groupes autour de 3-variétés/ Workshop on Groups around 3-Manifolds (Juin/June 05-16 2023)
Juin/June 12 :
Webpage : https://www.crmath.ca/en/activities/#/type/activity/id/3857
Program: https://crm.umontreal.ca/2023/3Manifolds/pdf/schedule-Manifolds-w2.pdf
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. We generalize the structure and the construction of the JSJ decomposition, to study the automorphisms of a (colorable) hierarchically hyperbolic group that satisfies some weak acylindricity conditions. The object that we construct can be viewed as a higher rank JSJ decomposition. Like the JSJ decomposition of a hyperbolic group it encodes information on the algebraic structure of the automorphism group and on the dynamics of individual automorphisms.
58:42
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic ...
published: 06 Sep 2021
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
- Report rights infringement
- published: 06 Sep 2021
- views: 713
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups.
Later, the JSJ was generalized to all finitely presented groups. In this generality it encodes the splittings but not all the automorphisms.
We further generalize the JSJ decomposition to study automorphisms of groups that act on products of hyperbolic spaces, and more generally to study automorphisms of (some) hierarchically hyperbolic groups (e.g. right angled Artin groups). The object that we construct can be viewed as a higher rank JSJ decomposition.
24:53
NCNGT2020: Volume Conjecture, geometric decomposition and deformation of hyperbolic structures (II)
Hi everyone! This to the second and the last talk of the series "Volume Conjecture, geomet...
published: 24 May 2020
NCNGT2020: Volume Conjecture, geometric decomposition and deformation of hyperbolic structures (II)
NCNGT2020: Volume Conjecture, geometric decomposition and deformation of hyperbolic structures (II)
- Report rights infringement
- published: 24 May 2020
- views: 88
Hi everyone! This to the second and the last talk of the series "Volume Conjecture, geometric decomposition and deformation of hyperbolic structures".
Last time, we discussed how the asymptotics of the quantum invariants for hyperbolic links and 3-manifolds are related to 3 dimensional hyperbolic geometry. This time, we will focus on some satellite links whose complements have more than one hyperbolic piece in the geometric decomposition, and relate the asymptotics of their colored Jones polynomials to the geometric structures on the geometric pieces.
Preprints are available on arxiv:
- Asymptotics of some quantum invariants of the Whitehead chains,
https://arxiv.org/abs/1912.10638
- Volume conjecture, geometric decomposition and deformation of hyperbolic structures
https://arxiv.org/abs/1912.11779
1:04:39
Benjamin Barrett: Gromov boundaries and Bowditch's JSJ decomposition
It is a fundamental principle in geometric group theory that large scale geometric propert...
published: 02 Apr 2021
Benjamin Barrett: Gromov boundaries and Bowditch's JSJ decomposition
Benjamin Barrett: Gromov boundaries and Bowditch's JSJ decomposition
- Report rights infringement
- published: 02 Apr 2021
- views: 222
It is a fundamental principle in geometric group theory that large scale geometric properties of metric spaces on which a group acts should be considered properties of the group itself. If a given group acts on a hyperbolic metric space, then a particularly natural example of such a large-scale property is the Gromov boundary of that space: this is a topological space that compactifies the hyperbolic space at infinity. Connectivity properties of this boundary tell us how we can cut the group up into simpler pieces: a famous theorem of Stallings says that the group splits (as an amalgamated product or HNN extension) over a finite group if and only if the boundary is disconnected. In fact, one can say more: work of Brian Bowditch tells us that the structure of the collection of local cut points in the boundary determines a canonical JSJ decomposition for the group. In this talk I'll describe how Bowditch's JSJ decomposition is built from the structure of the boundary.
47:44
Complexities of 3-manifolds
Knots and Spatial Graphs 2015
Complexities of 3-manifolds/ Jae Choon Cha (POSTECH)/ 2015-...
published: 24 May 2017
Complexities of 3-manifolds
Complexities of 3-manifolds
- Report rights infringement
- published: 24 May 2017
- views: 159
Knots and Spatial Graphs 2015
Complexities of 3-manifolds/ Jae Choon Cha (POSTECH)/ 2015-11-06
25:25
Symplectic fillings of lens spaces / Austin Christian / NCNGT 2021
Using the JSJ decomposition for symplectic fillings developed in our first talk, we comple...
published: 07 Jun 2021
Symplectic fillings of lens spaces / Austin Christian / NCNGT 2021
Symplectic fillings of lens spaces / Austin Christian / NCNGT 2021
- Report rights infringement
- published: 07 Jun 2021
- views: 29
Using the JSJ decomposition for symplectic fillings developed in our first talk, we complete the classification (up to diffeomorphism) of exact symplectic fillings of lens spaces. This is joint work with Youlin Li, and our result was independently obtained by John Etnyre and Agniva Roy.
This is the second of a pair of talks presented at NCNGT 2021. Here's the first: https://youtu.be/OQLa-E1bXCM
49:21
Martin Bobb: Decomposition along flats for convex projective manifolds
Real convex projective geometry generalizes hyperbolic geometry in a way that allows for i...
published: 26 Jun 2020
Martin Bobb: Decomposition along flats for convex projective manifolds
Martin Bobb: Decomposition along flats for convex projective manifolds
- Report rights infringement
- published: 26 Jun 2020
- views: 50
Real convex projective geometry generalizes hyperbolic geometry in a way that allows for interesting deformation theory and also aspects of non-positive curvature. In this talk I will introduce convex projective geometry, and we will discuss a natural decomposition of compact convex projective manifolds along their codimension-1 flat substructures. This extends a celebrated 2006 result of Benoist: a 'geometric JSJ-decomposition' for compact convex projective 3-manifolds to manifolds of every dimension (greater than 2).
1:04:05
"Conformal dimension and decompositions of hyperbolic groups," John Mackay, NYGT, 10/22/2021
"Conformal dimension and decompositions of hyperbolic groups," John Mackay (University of...
published: 22 Oct 2021
"Conformal dimension and decompositions of hyperbolic groups," John Mackay, NYGT, 10/22/2021
"Conformal dimension and decompositions of hyperbolic groups," John Mackay, NYGT, 10/22/2021
- Report rights infringement
- published: 22 Oct 2021
- views: 170
"Conformal dimension and decompositions of hyperbolic groups," John Mackay (University of Bristol), New York Group Theory Seminar, 10/22/2021
58:45
Geometry of complex surface singularities and 3-manifolds - Neumann
Geometric Structures on 3-manifolds
Topic: Geometry of complex surface singularities and 3...
published: 26 Jan 2016
Geometry of complex surface singularities and 3-manifolds - Neumann
Geometry of complex surface singularities and 3-manifolds - Neumann
- Report rights infringement
- published: 26 Jan 2016
- views: 2042
Geometric Structures on 3-manifolds
Topic: Geometry of complex surface singularities and 3-manifolds
Speaker: Walter Neumann
Date: Tuesday, January 26
I will talk about bilipschitz geometry of complex algebraic sets, focusing on the local geometry in dimension 2 (complex surface singularities), where the topological classification has long been understood in terms of 3-manifolds, while the analytic classification, even in this low dimension, is still very much out of reach. Bilipschitz geometry lies between the extremes of topological and analytic type. Although it leads to a "tame" classification (as first conjectured by Siebenmann and Sullivan in the 70's and proved by Mostowski in the mid-eighties), it is only in the last decade that the richness of the bilipschitz classification has become evident. I will describe work of Lev Birbrair, Anne Pichon and myself, on bilipschitz classification of complex surface germs in terms of refined JSJ decomposition of their 3-manifold links plus associated rational invariants, and if time permits, also the relationship of the classification with Zariski equisingularity, which was Zariski's approach to a tame classification.
For more videos visit http;//video.ias.edu
1:38:59
"Geometric Topology of 3-manifolds" by Prof. Krüger Ramos Álvaro (Part.2/4)
Abstract: One of the greatest achievements on mathematics in the 21st century is the proof...
published: 08 Dec 2022
"Geometric Topology of 3-manifolds" by Prof. Krüger Ramos Álvaro (Part.2/4)
"Geometric Topology of 3-manifolds" by Prof. Krüger Ramos Álvaro (Part.2/4)
- Report rights infringement
- published: 08 Dec 2022
- views: 58
Abstract: One of the greatest achievements on mathematics in the 21st century is the proof of the Poincaré's Conjecture by Grigory Perelman in 2003. Indeed, Perelman proved a much stronger result, which is the Geometrization Conjecture proposed by William Thurston in 1982. In order to do so, Perelman used the Ricci flow, a geometric/analytical argument proposed by Richard Hamilton. In this course, thought for a student with some background in Riemannian geometry, we will present Poincaré's conjecture in the context of the geometrization, explain the Geometrization theorem together with the eight Thurston's geometries and give an intuitive overview of the proof of Perelman.
☝️ Krüger Ramos Álvaro is professor at Universidade Federal do Rio Grande do Sul, Brazil.
This course was filmed at ICTP (Trieste, Italy) from October 24 to 27, 2022.
------------------------------------------------
Follow CIMPA news:
Website: https://www.cimpa.info
Facebook: https://bit.ly/3sY8OdQ
Twitter: https://twitter.com/cimpa_math
LinkedIn: https:https://bit.ly/3rHfrRs
JSJ decomposition
In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem:
The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson. The first two worked together, and the third worked independently.
The characteristic submanifold
An alternative version of the JSJ decomposition states:
The submanifold Σ with the smallest number of boundary tori is called the characteristic submanifold of M; it is unique (up to isotopy).
The boundary of the characteristic submanifold Σ is a union of tori that are almost the same as the tori appearing in the JSJ decomposition. However there is a subtle difference: if one of the tori in the JSJ decomposition is "non-separating", then the boundary of the characteristic submanifold has two parallel copies of it (and the region between them is a Seifert manifold isomorphic to the product of a torus and a unit interval). The set of tori bounding the characteristic submanifold can be characterised as the unique (up to isotopy) minimal collection of disjointly embedded incompressible tori such that closure of each component of the 3-manifold obtained by cutting along the tori is either atoroidal or Seifert-fibered.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/JSJ_decomposition
Zlil Sela: Automorphisms of groups and a higher ra...
Zlil Sela - Automorphisms of groups and a higher r...
NCNGT2020: Volume Conjecture, geometric decomposit...
Benjamin Barrett: Gromov boundaries and Bowditch's...
Complexities of 3-manifolds...
Symplectic fillings of lens spaces / Austin Christ...
Martin Bobb: Decomposition along flats for convex ...
"Conformal dimension and decompositions of hyperbo...
Geometry of complex surface singularities and 3-ma...
"Geometric Topology of 3-manifolds" by Prof. Krüge...
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jessie J
-
by Jesse Y Joy
-
by Jesse Y Joy
-
by Jesse Y Joy
-
by Jesse Y Joy
-
by Jesse Y Joy
-
by Jesse Y Joy
-
by Jesse & Joy
-
by Jesse & Joy
-
by Jesse & Joy
-
by Jesse & Joy
-
by Jesse & Joy
Nobody's Perfect
by: Jessie JWhen I'm nervous I have this thing yeah I talk too much
Sometimes I just can't shut the hell up
It's like I need to tell someone anyone who'll listen
And that's where I seem to fuck up, yeah
I forget about the consequences, for a minute there I lose my senses
And in the heat of the moment my mouth's starts going the words start flowing
But I never meant to hurt you, I know it's time that I learn to
Treat the people I love like I wanna be loved
This is a lesson learnt , I hate that I let you down and I feel so bad about it
I guess karma comes back around cause now I'm the one that's hurting yeah
And I hate that I made you think that the trust we had is broken
So don't tell me you can't forgive me
Cause nobody's perfect, no (x18) nobody's perfect
If I could turn back the hands of time
I swear I never would've crossed that line
I should of kept it between us but jessie went and told the whole world how I feel and oh
So I sit and I realise with these tears falling from my eyes
I gotta change if I wanna keep you forever
Promise that I'm gonna try
But I never meant to hurt you, I know it's time that I learn to
Treat the people I love like I wanna be loved
This is a lesson learnt and I hate that I let you down and I feel so bad about it I guess karma comes back around cause now I'm the one that's hurting yeah
And I hate that I made you think that the trust we had is broken so don't tell me you can't forgive me
Cause nobody's perfect, no, no, no, no, no, no, no,nobody's perfect
I'm not a saint no not at all, but what I did it wasn't cool
But I swear that I'll never do that again to you
I'm not a saint, no not at all, but what I did it wasn't cool
But I swear that I'll never do that again to you.
I hate that I let you down, and I feel so bad about it
I guess karma comes back around cause now I'm the one that's hurting yeah
And I hate that I made you think that that the trust we had is broken
So don't tell me you can't forgive me
Cause nobody's perfect, no,
And I hate that I let you down and I feel so bad about it
I guess karma comes back around and I'm the one that's hurting, yeah
And I hate that I made you think that the trust we had is broken
So don't tell me you can't forgive me
Cause nobody's perfect. yeah yeah
Don't tell me, don't tell me
No,no
You cant forgive