Arun Debray - Stable diffeomorphism classification of some unorientable 4-manifolds

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

Arun Debray, The University of Texas at Austin
Title: Stable diffeomorphism classification of some unorientable 4-manifolds
Abstract: Kreck's modified surgery theory provides a bordism-theoretic classification of closed, connected 4-manifolds up to stable diffeomorphism, i.e. up to diffeomorphism after connect-sum with some number of copies of S^2xS^2. For some classes of unorientable 4-manifolds with fundamental group pi_1 finite of order 2 mod 4, the classification question simplifies considerably, reducing to the case where . In this talk, I'll explain the generalities of Kreck's theorem and the ingredients that go into it, then specialize and give the classification in the case where pi_1 is finite of order 2 mod 4.