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Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Elder, Murray and McCammond, Jon and Meier, John (2003) Combinatorial conditions that imply word-hyperbolicity for 3-manifolds. Topology, 42 (6). pp. 1241-1259. ISSN 00409383

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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 piece-wise 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.

    Item Type: Article
    Subjects: 20-xx Group theory and generalizations
    57-xx Manifolds and cell complexes
    Faculty: UNSPECIFIED
    Depositing User: Dr Murray Elder
    Date Deposited: 17 Sep 2012 10:41
    Last Modified: 17 Sep 2012 10:41
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1081

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