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^2 x S^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 pi_1 = Z/2. 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. If time remains, I'll discuss what changes when one asks about the stable homeomorphism classification of topological 4-manifolds.

Mathematics

Audience: researchers in the topic

MIT Geometry and Topology Seminar

Series comments: Password is "topology".