Null-Homotopic Embedded Spheres of Codimenion One

Geometry Topology Student Seminar
Wednesday, September 27, 2017 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 006
Anubhav Mukherjee – Georgia Tech
Justin Lanier
Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.