Geometry & Topology, Vol. 8 (2004) Paper no. 13, pages 539--564.

The metric space of geodesic laminations on a surface: I

Xiaodong Zhu, Francis Bonahon

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

AMS subject classification. Primary: 57M99. Secondary: 37E35.

DOI: 10.2140/gt.2004.8.539

E-print: arXiv:math.GT/0308267

Submitted to GT on 9 October 2003. (Revised 16 March 2004.) Paper accepted 23 December 2004. Paper published 17 March 2004.

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Xiaodong Zhu, Francis Bonahon
NetScreen Technologies, 805 11-th Avenue
Building 3, Sunnyvale, CA 94089, USA
Department of Mathematics, University of Southern California
Los Angeles, CA 90089-1113, USA


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