Combinatorial conditions that imply word-hyperbolicity for 3-manifolds |
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Authors: | Murray Elder Jon McCammond John Meier |
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Institution: | a Department of Mathematics, Tufts University, Medford, MA 02155, USA b Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA c Department of Mathematics, Lafayette College, Easton, PA 18042, USA |
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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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Keywords: | 20F06 57M50 |
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