Jenya Sapir

A projection from geodesic currents to Teichmuller space

Given a genus g surface S, we consider the space of projective geodesic currents on S. This space contains many objects of interest in low dimensional topology, such as the set of all closed curves on S up to homotopy, the set of all marked, negatively curved metrics on S$, as well as some higher Teichmuller spaces. We show that there is a mapping class group invariant, length minimizing projection from the space of filling projective currents onto Teichmuller space, and that this projection is continuous and proper. This is joint work with Sebastian Hensel.