Asymptotics of Weil-Petersson geodesics I: ending laminations, recurrence, and flows

Details Asymptotics of Weil-Petersson geodesics I: ending laminations, recurrence, and flows Asymptotics of Weil-Petersson geodesics I: ending laminations, recurrence, and flows

2008-02-11

arxiv.org/abs/0802.1370v2

Mathematics

Geometric Topology

To appear, Geom. & Funct. Anal., referee's comments incorporated for final version

Scientific paper

We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric, these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and we show that the association of an ending lamination embeds asymptote classes of recurrent rays into the Gromov-boundary of the curve complex. As an application, we establish fundamentals of the topological dynamics of the Weil-Petersson geodesic flow, showing density of closed orbits and topological transitivity.

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