Member Seminar

Speaker: Lorenzo Riva, CMSA

Title: Un-extending extended TQFTs

Abstract: An ordinary topological quantum field theory (TQFT) assigns invariants to manifolds of dimensions n in a way that is compatible with cutting-and-gluing along submanifolds of dimension n-1. An extended TQFT assigns invariants that are also compatible with cutting along submanifolds of all codimensions. One way to formalize these notions is via functors between higher categories: an ordinary TQFT is a functor from a 1-category of (n-1)-dimensional manifolds and n-dimensional bordisms, while an extended TQFT is a functor from an n-category of k-dimensional manifolds (for k = 0, 1, … , n) each of which is a bordism between bordisms between bordisms between… and so on. It’s generally harder to deal with n-categories than it is to deal with 1-categories, so one might want to ask: can we reframe extended TQFTs in a 1-categorical context? We will answer this question during the talk.