Lengths are coordinates for convex structures

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Suppose that N is a geometrically finite orientable hyperbolic 3-manifold. Let P(N,C) be the space of all geometrically finite hyperbolic structures on N whose convex core is bent along a set C of simple closed curves. We prove that the map which associates to each structure in P(N,C) the lengths of the curves in the bending locus C is one-to-one. If C is maximal, the traces of the curves in C are local parameters for the representation space R(N).
46 pages, 3 figures; v2: corrections and improved exposition

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Geometric Topology, 30F40

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http://salesiana.dossiersoluciones.com/handle/123456789/71545

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0406257
 http://arxiv.org/abs/math/0406257

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arXiv