Lengths are coordinates for convex structures
Geometric Topology
2007-05-23 v2
Abstract
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).
Cite
@article{arxiv.math/0406257,
title = {Lengths are coordinates for convex structures},
author = {Young-Eun Choi and Caroline Series},
journal= {arXiv preprint arXiv:math/0406257},
year = {2007}
}
Comments
46 pages, 3 figures; v2: corrections and improved exposition