Construction of pseudo-isometries for treelike hyperbolic 3-manifolds of infinite volume |
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Authors: | Olivier Ly |
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Institution: | SchlumbergerSema, 36–38, rue de la Princesse, 78431 Louveciennes cedex, France |
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Abstract: | 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. To cite this article: O. Ly, C. R. Acad. Sci. Paris, Ser. I 337 (2003). |
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