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Quadric complexes. (English) Zbl 07244371
Summary: Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize \[2\]-dimensional \(\mathrm{CAT}(0)\) 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 \(\text{C}(4)\mbox{-}\text{T}(4)\) small cancelation groups act on quadric complexes.
MSC:
20F65 Geometric group theory
57M20 Two-dimensional complexes (manifolds) (MSC2010)
20F06 Cancellation theory of groups; application of van Kampen diagrams
05C12 Distance in graphs
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