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String Topology of Compact Symmetric Spaces

Philippe Kupper (KIT)

Monday, 2023-12-18 16:15

On the homology of the free loop space of a closed manifold M there exists the so-called Chas-Sullivan product. It is a product defined via the concatenation of loops and can, for example, be used to study closed geodesics of Riemannian or Finsler metrics on M. In this talk I will outline how one can use the geometry of symmetric spaces to partially compute the Chas-Sullivan product. In particular, we will see that the powers of certain non-nilpotent homology classes correspond to the iteration of closed geodesics in a symmetric metric. Some triviality results on the Goresky-Hingston cohomology product will also be mentioned. This talk is based on joint work with Maximilian Stegemeyer.