John Francis: Factorization homology and the cobordism hypothesis

Abstract : Factorization homology offers a multiplicative analogue of ordinary homology. Ordinary homology "integrates" an abelian group or chain complex over the moduli space of open subspaces of a manifold M. The result takes disjoint unions of manifolds to direct sums of chain complexes. Factorization homology "integrates" an n-disk algebra or higher category over the moduli space of stratifications of M. The result takes disjoint unions to tensor products. I'll give an introduction to factorization homology. Time permitting, I'll also discuss the cobordism hypothesis—after Baez–Dolan, Costello, Hopkins–Lurie, and Lurie—which asserts that for a suitable target C, there is an equivalence TQFT(C) = obj(C) between C-valued framed topological field theories and objects of C. I'll describe a proof of the cobordism hypothesis based on factorization homology. This is joint work with David Ayala.