Bucolic Complexes
Combinatorics
2018-12-10 v2 Group Theory
Metric Geometry
Abstract
We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study various approaches to bucolic complexes: from graph-theoretic and topological perspective, as well as from the point of view of geometric group theory. In particular, we characterize bucolic complexes by some properties of their 2-skeleta and 1-skeleta (that we call bucolic graphs), by which several known results are generalized. We also show that locally-finite bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties.
Cite
@article{arxiv.1202.1149,
title = {Bucolic Complexes},
author = {Bostjan Brešar and Jérémie Chalopin and Victor Chepoi and Tanja Gologranc and Damian Osajda},
journal= {arXiv preprint arXiv:1202.1149},
year = {2018}
}
Comments
45 pages, 4 figures