Year: 2017
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Hoda, Nima
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394645274