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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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

Keywords

Geometric Topology, Dynamical Systems, 30F60; 37D40

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/173896

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.1370
 http://arxiv.org/abs/0802.1370

Collections

arXiv