Word hyperbolic Dehn surgery
Abstract
Description
The aim of this paper is to demonstrate that very many Dehn fillings on a cusped hyperbolic 3-manifold yield a 3-manifold which is irreducible, atoroidal and not Seifert fibred, and which has infinite, word hyperbolic fundamental group. We establish an extension of the Thurston-Gromov $2π$ theorem by showing that if each filling slope has length more than six, then the resulting 3-manifold has all the above properties. We also give a combinatorial version of the $2π$ theorem which relates to angled ideal triangulations. We apply these techniques by studying surgery along alternating links.
49 pages, 26 figures. To appear in Inventiones Mathematicae. Revised version, incorporating referee's comments. Most changes are minor; the proof of Theorem 4.7 has been corrected
49 pages, 26 figures. To appear in Inventiones Mathematicae. Revised version, incorporating referee's comments. Most changes are minor; the proof of Theorem 4.7 has been corrected