English

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