Geometry
Construction of pseudo-isometries for treelike hyperbolic 3-manifolds of infinite volume
Comptes Rendus. Mathématique, Volume 337 (2003) no. 7, pp. 457-460.

We introduce a family of rigid hyperbolic 3-manifolds of infinite volume with possibly infinitely many ends: the treelike manifolds. These manifolds generalize a family of constructive non compact surfaces – the equational surfaces – for which the homeomorphism problem is decidable. The proof of rigidity relies firstly on Thurston's theorem of compactness of the Teichmüller space of acylindrical compact 3-manifolds, and secondly, on Sullivan's rigidity theorem.

Nous introduisons une famille de 3-variétés hyperboliques rigides de volume infini à nombre de bouts infini : les variétés arborescentes. Ces variétés généralisent une famille de surfaces non compactes constructives – les surfaces équationnelles – pour lesquelles le problème de l'homéomorphisme est décidable. La démonstration de rigidité s'appuie sur, premièrement, le théorème de Thurston de compacité de l'espace de Teichmüller des 3-variétés compactes acylindriques, et deuxièmement, le théorème de rigidité de Sullivan.

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DOI: 10.1016/j.crma.2003.08.005
Ly, Olivier 1

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Ly, Olivier. Construction of pseudo-isometries for treelike hyperbolic 3-manifolds of infinite volume. Comptes Rendus. Mathématique, Volume 337 (2003) no. 7, pp. 457-460. doi : 10.1016/j.crma.2003.08.005. http://www.numdam.org/articles/10.1016/j.crma.2003.08.005/

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