Geometric Factorization Algebras

Abstract

Let M be a smooth manifold and let Open(M) denote the operad on inclusions and disjoint open subsets. This dissertation is concerned with converting the classical factorization algebra construction built on Open(M) to the geometric setting. That is, we consider each object in our operads (analogs of Open(M)) equipped with its own geometry. We build a formalism around these novel geometric operads and study the notion of a geometric factorization algebra along with geometric factorization homology..