1999/01/11 by Carlo Petronio, Joan Porti, Petronio, Carlo +1 · 51 citations
Computer Science · Mathematics · #57M50 (primary) #57Q15 (secondary) #Combinatorics #Dehn surgery #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Hyperbolic 3-manifold #Hyperbolic function #Hyperbolic group #Hyperbolic manifold #Ideal (ethics) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Smoothness #Triangulation #math.GT #msc:57M50 #msc:57Q15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/9901045
published in arXiv (Cornell University) (Cornell University) · 23 pages, 4 figures, Latex
arxiv created 1999/01/11 · openalex publication_date 1999/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.