CAT(0) is an algorithmic property
Geometric Topology
2012-05-16 v1 Group Theory
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.
Cite
@article{arxiv.math/0301056,
title = {CAT(0) is an algorithmic property},
author = {Murray Elder and Jon McCammond},
journal= {arXiv preprint arXiv:math/0301056},
year = {2012}
}
Comments
(23 pages) To appear in Geometriae Dedicata