Quadric Complexes
Group Theory
2019-11-27 v4
Abstract
Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study the basic properties of these complexes. Using a form of dismantlability for the 1-skeleta of finite quadric complexes we show that every finite group acting on a quadric complex stabilizes a complete bipartite subgraph of its 1-skeleton. Finally, we prove that C(4)-T(4) small cancellation groups act on quadric complexes.
Cite
@article{arxiv.1711.05844,
title = {Quadric Complexes},
author = {Nima Hoda},
journal= {arXiv preprint arXiv:1711.05844},
year = {2019}
}
Comments
27 pages, 9 figures; to appear in Michigan Mathematical Journal