A Proof of the 1-Dimensional Cobordism Hypothesis, using Hochschild Homology
Talk by Dr. David Ayala (Mathematical Sciences, MSU)
03/12/2021 4:10-5:15pm Zoom Meeting
Abstract: The n-dimensional cobordism hypothesis asserts a classification of scale-invariant n-dimensional quantum field theories (TQFTs). These are physics-y words for a classification of representations of a category of (n-1)-manifolds and n-dimensional cobordisms between them.
In this talk, we’ll make this assertion explicit, and outline a proof of it, in the cases that n=0 and n=1.
- In the case n=0, both the assertion and its proof are relatively simple, though complex enough to display some nuance. In particular, classifying spaces of symmetric groups, and the sphere spectrum, pop up.
- In the case n=1, the assertion is relatively simple. Its proof is reasonable enough imagine, though some simple observations reveal overwhelming complexity. I’ll explain how to use Hochschild homology, or factorization homology over a circle, to manage this complexity, for a proof of the assertion in this n=1 case.
This is part of joint work with John Francis.