Combinatorial conditions that imply word-hyperbolicity for 3-manifolds
Geometric Topology
2012-05-16 v1 Group Theory
Abstract
Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston's conjecture by proving that such a manifold admits a piecewise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The proof involves a mixture of computer computation and techniques from small cancellation theory.
Cite
@article{arxiv.math/0301057,
title = {Combinatorial conditions that imply word-hyperbolicity for 3-manifolds},
author = {Murray Elder and Jon McCammond and John Meier},
journal= {arXiv preprint arXiv:math/0301057},
year = {2012}
}
Comments
(21 pages) To appear in Topology