What do closed strings know about the space they live on?

by Prof. Nathalie Wahl (University of Copenhagen)

Thursday 3 Nov 2022, 14:00 → 15:00 Europe/Brussels

Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve)

To a Riemannian manifold M, one can associate the space LM of all closed strings in M. By classical Morse theory, the homology of this second space is build out of closed geodesics in M. String topology, as introduced 20 years about by Chas and Sullivan, can be thought of as a refinement of the homology LM, remembering the extra information of how strings can sometimes be concatenated or cut. I'll give an introduction to string topology, and to what this extra structure on LM knows about M.