CAT(0) is an Algorithmic Property

Elder, Murray and McCammond, Jon (2004) CAT(0) is an Algorithmic Property. Geometriae Dedicata, 107 (1). pp. 25-46. ISSN 0046-5755

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    In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is non-positively curved. In particular, given such a complex we show how to define a boolean combination of polynomial equations and inequalities in real variables, i.e. a real semi-algebraic set, which is empty if and only if the complex is non-positively curved. Once this equivalence has been shown, the main result follows from a standard theorem in real algebraic geometry.

    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

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