On regular CAT(0) cube complexes and the simplicity of automorphism groups of rank-one CAT(0) cube complexes (Q2412929)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On regular CAT(0) cube complexes and the simplicity of automorphism groups of rank-one CAT(0) cube complexes |
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On regular CAT(0) cube complexes and the simplicity of automorphism groups of rank-one CAT(0) cube complexes (English)
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6 April 2018
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Summary: We provide a necessary and sufficient condition on a finite flag simplicial complex \(L\) for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to \(L\). We then find new examples of such CAT(0) cube complexes and prove that their automorphism groups are virtually simple. The latter uses a result, which we prove in the appendix, about the simplicity of certain subgroups of the automorphism group of a rank-one CAT(0) cube complex. This result generalizes previous results by \textit{J. Tits} [in: Essays on topology and related topics. Mémoires dédiés à Georges de Rham. Berlin-Heidelberg-New York: Springer-Verlag. 188--211 (1970; Zbl 0214.51301)] and by \textit{F. Haglund} and \textit{F. Paulin} [Geom. Topol. Monogr. 1, 181-248 (1998; Zbl 0916.51019)].
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non-positive curvature
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cube complexes
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Coxeter groups
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regular complexes
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simple groups
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