Algebra/Topology seminar
Speaker: Xuija Chen
Title: Kontsevich’s invariants as topological invariants of configuration space bundles
Abstract: Kontsevich's invariants (also called “configuration space integrals”) are invariants of certain framed smooth manifolds/fiber bundles/knots. The result of Watanabe(2018) showed that Kontsevich’s invariants can distinguish smooth fiber bundles that are isomorphic as topological fiber bundles. I will first give an introduction to Kontsevich's invariants, and then state my work which provides a perspective on how to understand their ability of detecting exotic smooth structures: real blow up operations essentially depend on the smooth structure, so, given a space/bundle X, the topology of some spaces/bundles obtained by doing some real blow-ups on X can be different for different smooth structures on X.