/ Xujia Chen: Kontsevich’s invariants as topological invariants of configuration space bundles

Xujia Chen: Kontsevich’s invariants as topological invariants of configuration space bundles

September 26, 2023
4:30 pm - 5:30 pm

Abstract: Kontsevich’s invariants (also called “configuration space integrals”) are invariants of certain framed smooth manifolds/fiber bundles. The result of Watanabe(’18) 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 depends on the smooth structure, and thus given a space/bundle X, the topological invariants of some spaces/bundles obtained by doing some real blow-ups on X can be different for different smooth structures on X.