Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The metric space of geodesic laminations on a surface: I

Xiaodong Zhu and Francis Bonahon

Geometry & Topology 8 (2004) 539–564

arXiv: math.GT/0308267

Abstract

We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric dH and with a variation of this metric called the dlog 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