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CAT(0) is an algorithmic property

Murray Elder·Jon McCammond
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Abstract

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.

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Murray Elder, Jon McCammond. 2003-01-07. CAT(0) is an algorithmic property. https://doi.org/10.1023/b%3Ageom.0000049096.63639.e3

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