Free Loop Spaces and Topological coHochschild Homology

Anna Marie Bohmann (Vanderbilt University)

Resumen: Free loop spaces arise in many areas of geometry and topology. Simply put, the free loops on a space X is the space of maps from the circle into X. This is a main object of study in string topology and has important connections to geodesics on manifolds. In this talk, we discuss a new approach to computing the homology of free loop spaces via topological coHochschild homology, which is an invariant of coalgebras arising from homotopy theory techniques. This approach produces a spectral sequence for the homology of free loop spaces with algebraic structure that allows us to make new computations. This is joint work with Teena Gerhardt and Brooke Shipley.