The metric space of geodesic laminations on a surface: I

Zhu, Xiaodong¹ ; Bonahon, Francis²

¹ NetScreen Technologies, Building 3, 805 11th Avenue, Sunnyvale, California 94089, USA
² Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113, USA

Geometry & topology, Tome 8 (2004) no. 2, pp. 539-564.

Résumé

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.

Détail

DOI : 10.2140/gt.2004.8.539

Keywords: Geodesic lamination, simple closed curve

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