# Bijections of geodesic lamination space preserving left Hausdorff convergence

Abstract : We introduce an asymmetric distance function, which we call the left Hausdorff distance function", on the space of geodesic laminations on a closed hyperbolic surface of genus at least 2. This distance is an asymmetric version of the Hausdorff distance between compact subsets of a metric space. We prove a rigidity result for the action of the extended mapping class group of the surface on the space of geodesic laminations equipped with the topology induced from this distance. More specifically, we prove that there is a natural homomorphism from the extended mapping class group into the group of bijections of the space of geodesic laminations that preserve left Hausdorff convergence and that this homomorphism is an isomorphism.
Keywords :
Type de document :
Pré-publication, Document de travail
2018
Domaine :

https://hal.archives-ouvertes.fr/hal-01782032
Soumis le : mardi 11 décembre 2018 - 05:13:53
Dernière modification le : mercredi 12 décembre 2018 - 01:22:13

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hausdorff-8.pdf
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### Identifiants

• HAL Id : hal-01782032, version 2
• ARXIV : 1805.00764

### Citation

Ken'Ichi Ohshika, Athanase Papadopoulos. Bijections of geodesic lamination space preserving left Hausdorff convergence. 2018. 〈hal-01782032v2〉

### Métriques

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