Algebra/Topology seminar

Speaker: Noah Porcelli

Abstract: String topology is the study of algebraic operations on free loop spaces of manifolds. This includes the structure of both a product and a coproduct. In contrast to the product, Naef showed that the coproduct is surprisingly not a homotopy invariant of a manifold: string topology ``sees'' more than just the homotopy type. We classify the failure for the coproduct to be a homotopy invariant, in terms of an invariant coming from K-theory of spaces. Similar answers have also been obtained by Naef-Safronov and Wahl, in terms of slightly different invariants.