The metric space of geodesic laminations on a surface: I

Zhu, Xiaodong; Bonahon, Francis

doi:10.2140/gt.2004.8.539

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The metric space of geodesic laminations on a surface: I

Xiaodong Zhu and Francis Bonahon

Geometry & Topology 8 (2004) 539–564

DOI: 10.2140/gt.2004.8.539

arXiv: math.GT/0308267

Abstract

We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric $d_{H}$ and with a variation of this metric called the $d_{log}$ metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these two metrics to another metric which is combinatorially defined in terms of train tracks.

Keywords

Geodesic lamination, simple closed curve

Mathematical Subject Classification 2000

Primary: 57M99

Secondary: 37E35

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Publication

Received: 9 October 2003

Revised: 16 March 2004

Accepted: 23 December 2004

Published: 17 March 2004

Proposed: Jean-Pierre Otal

Seconded: David Gabai, Martin Bridson

Authors

Xiaodong Zhu
NetScreen Technologies Building 3 805 11th Avenue Sunnyvale California 94089 USA

Francis Bonahon
Department of Mathematics University of Southern California Los Angeles California 90089-1113 USA

Volume 8, issue 2 (2004)