English

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.

Keywords

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