Factorization Homology for Embedded Submanifolds

Abstract

In this thesis I will explore the theory of factorization homology including prerequisitematerial required to understand the definitions and structures used in the theory. I will beginwith a brief survey of some basic structures in infinity category theory. Using these toolsI will explore the theory of stratified spaces and how it pertains to factorization homology.Once we have built the symmetric monoidal∞-categoriesSnglr,Bsc, andMfld(B) wecan then define factorization homology. From there we will explore factorization homologyfor embedded submanifolds. The goal of this work is to build a notion of factorizationhomology for sutured manifolds. This will serve as the first steps in my PhD work withMarcy Robertson at The University of Melbourne.