Abstract

This talk will explain factorization homology, which is intended to abstract and organize the observables of a TQFT. Factorization homology is a construction that associates a chain complex to a (framed) n-manifold M and a (rigid) n-category C. One can rightfully think of C as the domain of a topological QFT, and C as an organization of point/line/surface/… observables of the QFT as they interact with one another. I will explain several pleasant features of factorization homology, and outline how these features alone can be used to work with factorization homology. I will identify a few values of factorization homology, which recover some familiar invariants of quantum topology (ie, the Jones polynomial and Skein modules). Much of this theory has yet to be fully developed. I will be clear about which aspects can be found in literature and which are more speculative. All of this work is joint with John Francis.