Special Colloquium
Aliakbar Daemi
Columbia University
Exotic Structures, Homology Cobordisms and Chern-Simons Functional
Abstract: An exotic structure on a smooth manifold X is another smooth manifold which is homeomorphic but not diffeomorphic to X. There are many closed 4-manifolds which admit exotic smooth structures. However, it is still an open question whether there are exotic structures on simple closed 4-manifolds such as the 4-dimensional sphere (smooth Poincare conjecture) and S^1xS^3. Motivated by the latter case, Akbulut asked whether there are an integral homology sphere Y with non-trivial Rokhlin invariant and a simply connected homology cobordism from Y to itself. In this talk, I will introduce various invariants of homology cobordism classes of 3-manifolds and discuss some of their topological applications. In particular, we answer Akbulut’s question for various integral homology spheres and propose a plan to completely address his conjecture.
Followed by mini-tea in 636 SEO from 4:00pm to 4:15pm.
Friday May 3, 2019 at 3:00 PM in 636 SEO