Geometry and Topology Seminar

In hyperbolic space, the unit tangent bundle has a foliation by horospheres, which are exponentially contracted by the geodesic flow as a function of time. We show that the same behavior holds in the universal cover of the moduli space of Riemann surfaces, endowed with the Teichmüller metric, except possibly when geodesics spend too much time in the cusps of moduli space. (It is known that this behavior can fail in the cusps.)