Topology Seminar: Aliakbar Daemi

It is an open problem whether there exists an exotic smooth structure on S^1 × S^3. Motivated by this problem, Akbulut asked if there is a simply connected homology cobordism from a homology sphere with non-trivial Rochlin invariant to itself. The main progress toward this question was made by Taubes who used his celebrated technique of gauge theory on manifolds with periodic ends to give a negative answer to this question for various homology spheres including the Poincare homology sphere. In this talk, I will present a different technique which can be used to generalize Taubes' result in various directions. In particular, we address Akbulut's question for a family of Brieskorn homology spheres, which is not covered by Taubes' theorem.