Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize -dimensional 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 -skeleta of finite quadric complexes, we show that every finite group acting on a quadric complex stabilizes a complete bipartite subgraph of its -skeleton. Finally, we prove that small cancelation groups act on quadric complexes.
"Quadric Complexes." Michigan Math. J. 69 (2) 241 - 271, May 2020. https://doi.org/10.1307/mmj/1576832418