Posts about Algebraic topology
EDIT: I've gotten a bunch of responses, which is great! I think I've responded to everyone, but if you sent me a chat or a message and I didn't respond, please try again. Everyone who messages me gets the invite, so if you didn't get one, it's just because I'm dumb and didn't see the message. :-)
Hi everyone! My name is Joe and I have a doctorate in mathematics where I studied Homotopy Theory and Homological Algebra.
A few friends and I have been meeting once per week for a topology "study group", for lack of a better thing to call it. We work through a text, ask questions, do exercises, and try to support each other as we learn. The exact structure of the meetings changes depending on who is attending, as a lot of people come and go based on content and their personal lives.
We're about to start a new topic, so I thought it would be a good time to invite other people to join us! We're starting Algebraic Topology using Allen Hatcher's book (which he gives out for free). We meet for two hours on Sundays at 11am EDT (3pm GMT). We meet over voice chat with some screen-sharing; you're free to join the conversation or just listen if you want. (Sometimes people don't have microphones.) It's a pretty small group but we try not to single anyone out.
Send me a PM if you want to join and I'll get you an invite to the server! Everyone is welcome, I just don't think it's a good idea to put server invites in permanent posts. I'll be checking in on this post and on my PM's throughout the day.
Note: Don't worry too much about "prerequisites". If you have an inquisitive mind and want to come check it out then you should do that. It's not a class, so you can come and go as you please. However, to get the most out of Hatcher's book, you'd ideally have some experience with proof-based mathematics and know some point-set topology.
Hope to see you tomorrow!
Next semester I will be taking an AT course, and I wanted to also do a guided reading project based on a related topic. I have already studied some AT on my own and liked it a lot, so I want something of a similar flavor but without much overlap with the course.
What motivated me to take up this project was reading about the KKM Lemma and equivalent results like Brouwer's Fixed Point Theorem and Sperner's Lemma. These are the kinds of results I would like to learn about in the project, but I don't know where I can find enough such results to be able to fill up a semester-long project.
My guide has suggested reading 'Geometry of Surfaces' by Stilwell or 'The Knot Book' by Adams, but he is open to anything else I might like. Do you have any suggestions for topics/books I could look into?
