Topology Seminar by Nathan Perlmutter

Extra topology seminar.

Speaker: Nathan Perlmutter (Stanford)

Title: Cobordism categories and the moduli space of odd dimensional manifolds

Abstract: In this talk I will present recent joint work of mine with Fabian Hebestreit where we prove that certain stable moduli spaces of odd dimensional manifolds are homology equivalent to infinite loopspaces. The main novel ingredient in our work is a version of the cobordism category incorporating surgery data in the form of Lagrangian subspaces. Our main result can be viewed as the first step toward obtaining an analogue of the Madsen-Weiss theorem for odd dimensional manifolds.