Negatively Oriented Ideal Triangulations and a Proof of Thurston's Hyperbolic Dehn Filling Theorem
Geometric Topology
2007-05-23 v1
Abstract
We give a complete proof of Thurston's celebrated hyperbolic Dehn filling theorem, following the ideal triangulation approach of Thurston and Neumann-Zagier. We avoid to assume that a genuine ideal triangulation always exists, using only a partially flat one, obtained by subdividing an Epstein-Penner decomposition. This forces us to deal with negatively oriented tetrahedra. Our analysis of the set of hyperbolic Dehn filling coefficients is elementary and self-contained. In particular, it does not assume smoothness of the complete point in the variety of deformations.
Keywords
Cite
@article{arxiv.math/9901045,
title = {Negatively Oriented Ideal Triangulations and a Proof of Thurston's Hyperbolic Dehn Filling Theorem},
author = {Carlo Petronio and Joan Porti},
journal= {arXiv preprint arXiv:math/9901045},
year = {2007}
}
Comments
23 pages, 4 figures, Latex