CAT(0) is an algorithmic property

Publication Type:
Journal Article
Geometriae Dedicata, 2004, 107 (1), pp. 25 - 46
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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 nonpositively 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 nonpositively curved. Once this equivalence has been shown, the main result follows from a standard theorem in real algebraic geometry. © 2004 Kluwer Academic Publishers.
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