Cobordism categories and moduli spaces of odd dimensional manifolds

摘要

We prove that the stable moduli space of (n - 1)-connected, n-parallelizable, (2n + 1)-dimensional manifolds is homology equivalent to an infinite loopspace for n >= 4, n not equal 7. The main novel ingredient is a version of the cobordism category incorporating surgery data in the form of Lagrangian subspaces. (C) 2019 Published by Elsevier Inc.