My fourteenth Math Research Livestream is now available on YouTube:

https://www.youtube.com/watch?v=pVoFfZAyXzk

I talked about some topics related to my recent preprint (https://arxiv.org/abs/2409.12923) about topological lattices.

I decided to skip streaming today because I wanted to talk about polyhedral products, but I haven't found the old calculation that I wanted to talk about yet. Shocking I couldn't find something I did like six years ago in the ten minutes before I would start streaming. I'll look for it now, so hopefully I'll be ready next week.

#math #topology #algebra #AbstractAlgebra #UniversalAlgebra #combinatorics #LatticeTheory

I'll be streaming again in 20 minutes at twitch.tv/charlotteaten. I'll be talking about my recent preprint (https://arxiv.org/abs/2409.12923) about topological lattices!

#math #topology #algebra #AbstractAlgebra #UniversalAlgebra #combinatorics #LatticeTheory

I posted a new paper on the arXiv!

https://arxiv.org/abs/2409.12923

In "Higher-dimensional book-spaces" I show that for each \(n\) there exists an \(n\)-dimensional compact simplicial complex which is a topological modular lattice but cannot be endowed with the structure of topological distributive lattice. This extends a result of Walter Taylor, who did the \(2\)-dimensional case.

I think this kind of result is interesting because we can see that whether spaces continuously model certain equations is a true topological invariant. All of the spaces that I discuss here are contractible, but only some can have a distributive lattice structure.

A similar phenomenon happens with H-spaces. The \(7\)-sphere is an H-space, and it is even a topological Moufang loop, but it cannot be made into a topological group, even though our homotopical tools tell us that it "looks like a topological group".

This is (a cleaned up version of) something I did during my second year of graduate school. It only took me about six years to post it.

#math #topology #algebra #AbstractAlgebra #UniversalAlgebra #combinatorics #LatticeTheory

I'll be streaming again in 15 minutes at https://www.twitch.tv/charlotteaten. I'm gonna keep talking about topological lattices, since I've realized some new things since last week.

#math #livestream #Twitch #topology #research #UniversalAlgebra #AbstractAlgebra #algebra #LatticeTheory #CategoryTheory

My twelfth Math Research Livestream is now available on YouTube:

https://youtu.be/W3oXOS4Yx6k

This time, I talked about this paper (https://arxiv.org/abs/1602.00034) by George Bergman. I have something related which I've finally decided to post to the arXiv, so hopefully I'll be ready to talk about that preprint next week.

#math #livestream #Twitch #topology #research #UniversalAlgebra #AbstractAlgebra #algebra #LatticeTheory #CategoryTheory

I'll be streaming again in 20 minutes at https://www.twitch.tv/charlotteaten. This week I'm going to switch gears and talk about this paper (https://arxiv.org/abs/1602.00034) of George Bergman. I have something related which I've finally decided to post to the arXiv, so hopefully this will prepare me to talk about that new preprint next week.

#math #livestream #Twitch #topology #research #UniversalAlgebra #AbstractAlgebra #algebra #LatticeTheory #CategoryTheory