#### Volume 8, issue 2 (2004)

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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
 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
Primary: 57M99
Secondary: 37E35
##### 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