Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Title: Combinatorial conditions that imply word-hyperbolicity for 3-manifolds
Creator: Elder, Murray; McCammond, Jon; Meier, John
Relation: Topology Vol. 42, Issue 6, p. 1241-1259
Publisher Link: http://dx.doi.org/10.1016/S0040-9383(02)00100-3
Publisher: Elsevier
Resource Type: journal article
Date: 2003
Description: 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.
Subject: three-manifolds; word-hyperbolic; non-positive curvature; CAT(0)
Identifier: http://hdl.handle.net/1959.13/930971
Identifier: uon:10972
Identifier: ISSN:0040-9383
Language: eng
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