Negatively Oriented Ideal Triangulations and a Proof of Thurston's Hyperbolic Dehn Filling Theorem

Carlo Petronio; Joan Porti

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arXiv · math/9901045

Negatively Oriented Ideal Triangulations and a Proof of Thurston's Hyperbolic Dehn Filling Theorem

Carlo Petronio·Joan Porti

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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.

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BibTeX RIS

Carlo Petronio, Joan Porti. 1999-01-11. Negatively Oriented Ideal Triangulations and a Proof of Thurston's Hyperbolic Dehn Filling Theorem. https://arxiv.org/abs/math/9901045

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