CAT(0) cubical complexes for graph products of finitely generated abelian groups

zbMATH Open1380.20043arXiv1310.8646MaRDI QIDQ739866

Stefan Witzel, Kim Ruane

Publication date: 11 August 2016

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Abstract: We show that every graph product of finitely generated abelian groups acts properly and cocompactly on a CAT(0) cubical complex. The complex generalizes (up to subdivision) the Salvetti complex of a right-angled Artin group and the Coxeter complex of a right-angled Coxeter group. In the right-angled Artin group case it is related to the embedding into a right-angled Coxeter group described by Davis and Januszkiewicz. We compare the approaches and also adapt the argument that the action extends to finite index supergroup that is a graph product of finite groups.

Full work available at URL: https://arxiv.org/abs/1310.8646

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zbMATH Keywords

graph productscubical complexes

Mathematics Subject Classification ID

Geometric group theory (20F65) Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Topological methods in group theory (57M07) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (7)

The Furstenberg–Poisson boundary and CAT(0) cube complexes ⋮ Amenable covers of right‐angled Artin groups ⋮ Automorphisms of graph products of groups and acylindrical hyperbolicity ⋮ Coarse cubical rigidity ⋮ Divergence of CAT(0) cube complexes and Coxeter groups ⋮ Actions of Cremona groups on CAT\((0)\) cube complexes ⋮ Unnamed Item

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