Maximilian Stegemeyer - Intersection multiplicity in loop spaces and the string topology coproduct

Abstract: String topology is the study of algebraic structures on the free loop space of a closed oriented manifold. The Goresky-Hingston coproduct is geometrically defined by cutting loops apart at points of self-intersection. A result by Hingston and Wahl makes this intuitive description precise and sates that if a homology class can be represented by loops without basepoint self-intersections then the coproduct of this class vanishes. In this talk I will talk about some results where the concept of intersection multiplicity is used to conclude the triviality of the string topology coproduct. We will also encounter the relation between the homology of the free loop space and the closed geodesics in the underlying manifold. The triviality results for the coproduct open up a number of questions.