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Curvature testing in 3-dimensional metric polyhedral complexes

Elder, Murray and McCammond, Jon (2002) Curvature testing in 3-dimensional metric polyhedral complexes. Experiment. Math., 11 (1). pp. 143-158.

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    Abstract

    In a previous article, the authors described an algorithm to determine whether a �nite metric polyhedral complex satis�ed various local curvature conditions such as being locally CAT(0). The proof made use of Tarski's theorem about the decidability of �rst order sentences over the reals in an essential way and thus was not immediately applicable to a speci�c �nite complex. In this article we describe an algorithm restricted to 3-dimensional complexes which uses only elementary 3-dimensional geometry. After describing the procedure we include several examples involving Euclidean tetrahedra which were run using an implementation of the algorithm in GAP.

    Item Type: Article
    Subjects: 20-xx Group theory and generalizations
    Faculty: UNSPECIFIED
    Depositing User: Dr Murray Elder
    Date Deposited: 17 Sep 2012 10:42
    Last Modified: 17 Sep 2012 10:42
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1210

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