Geodesics in CAT(0) Cubical Complexes
Combinatorics
2015-03-17 v1 Computational Geometry
Discrete Mathematics
Metric Geometry
Abstract
We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed any interval in the integer lattice cubing of its dimension.
Cite
@article{arxiv.1101.2428,
title = {Geodesics in CAT(0) Cubical Complexes},
author = {Federico Ardila and Megan Owen and Seth Sullivant},
journal= {arXiv preprint arXiv:1101.2428},
year = {2015}
}
Comments
27 pages, 7 figures