Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Murray Elder; Jon McCammond; John Meier

doi:10.1016/s0040-9383(02)00100-3

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Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Murray Elder·Jon McCammond·John Meier

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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.

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Murray Elder, Jon McCammond, John Meier. 2003-01-07. Combinatorial conditions that imply word-hyperbolicity for 3-manifolds. https://doi.org/10.1016/s0040-9383(02)00100-3

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