[Geometry, Topology and Dynamics Seminar] Non-smoothable bundles and gauge theory for families by Dr. Hokuto Konno (Riken)

Abstract: It is known that there exist many "non-smoothable 4-manifolds", that is, topological 4-manifolds which do not admit smooth manifold structures. Gauge theory provides a strong tool to detect such interesting topological 4-manifolds. In this talk, I will explain a family version of this story. Namely, I will show that a family version of gauge theory may detect "non-smoothable 4-manifold bundles", which is a fiber bundle whose structure group is the homeomorphism group of a 4-manifold, but we cannot reduce the structure group into the diffeomorphism group. This is joint work with David Baraglia and with Tsuyoshi Kato and Nobuhiro Nakamura.