Ending laminations for Weil-Petersson geodesics

Babak Modami (Yale)

Abstract: The Weil-Petersson (WP) metric is an incomplete Riemannian metric on the moduli space of Riemann surfaces with negative sectional curvatures which are not bounded away from 0. Brock, Masur and Minsky introduced a notion of "ending lamination" for WP geodesic rays which is an analogue of the vertical foliations of Teichmuller geodesics. In this talk we show that these laminations and the associated subsurface coefficients can be used to determine the itinerary of a class of WP geodesics in the moduli space. As a result we give examples of closed WP geodesics staying in the thin part of the moduli space, geodesic rays recurrent to the thick part of the moduli space and diverging geodesic rays. These results can be considered as a kind of symbolic coding for WP geodesics.