Topology and Geometric Group Theory Seminar
Tuesday, October 6, 2020 - 1:30pm
Via Zoom
An exotic sphere is a smooth and oriented manifold homeomorphic, but not necessarily diffeomorphic, to a sphere.
If M is any other smooth and oriented manifold we may form the connected sum of M with an exotic sphere.
This does not change the homeomorphism type of M, but may change the smooth structure.
I will explain work, joint with Robert Burklund and Andrew Senger, that explores this construction when M is in the "metastable range," or more precisely when the first non-trivial homology group of M is in degree at least one-third the dimension of M. We find connections with the Adams spectral sequence that computes the stable homotopy groups of spheres.
Introductory talk at 1:30pm by J.D. Quigley. Seminar talk at 2pm.