Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Details Combinatorial conditions that imply word-hyperbolicity for 3-manifolds Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

2003-01-07

arxiv.org/abs/math/0301057v1

Mathematics

Geometric Topology

(21 pages) To appear in Topology

Scientific paper

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.

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