Alexandra Ballow
Montana State University
Title
A Combinatorial Approach to Factorization Homology
Abstract
We aim to integrate a 2-category over a (framed) surface using combinatorics. In other words, we define a purely combinatorial implementation of factorization homology. We will begin with an intuitive discussion of what factorization homology is. Throughout this discussion we will focus on a combinatorial description of factorization homology over the circle. This simpler construction will inform how we approach the 2 dimensional case. There are several challenges in extending this definition, including the need to define 2-dimensional quivers. We finish with some applications, particularly the correspondence between factorization homology of a surface and Turaev-Viro on surfaces.
