Speaker: Ali Daemi, Washington University
Title: 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.
Friday, November 22, 2019 at 2:30pm to 3:20pm
S1063, S 1063