CAT(0) is an algorithmic property

Details CAT(0) is an algorithmic property CAT(0) is an algorithmic property

2003-01-07

arxiv.org/abs/math/0301056v1

Mathematics

Geometric Topology

(23 pages) To appear in Geometriae Dedicata

Scientific paper

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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