An upper bound for the volumes of complements of periodic geodesics

2014/12/08 by Maxime Bergeron, Bergeron, Maxime, Tali Pinsky +3
Mathematics · #20F65 (secondary) #57M27 (primary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20F65 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1412.2446

Reworked arguments and improved figures. 20 pages, 12 figures

arxiv created 2016/05/10 · arxiv updated 2016/05/11

Abstract

A periodic geodesic on a surface has a natural lift to the unit tangent bundle; when the complement of this lift is hyperbolic, its volume typically grows as the geodesic gets longer. We give an upper bound for this volume which is linear in the geometric length of the geodesic.

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