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Special cube complexes revisited: a quasi-median generalization

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  11 April 2022

Anthony Genevois
Anthony Genevois*
Affiliation:
Montpellier Alexander Grothendieck Institute, Université de Montpellier, Place Eugène Bataillon, 34090 Montpellier, France
*
e-mail: anthony.genevois@umontpellier.fr
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Abstract

In this article, we generalize Haglund and Wise’s theory of special cube complexes to groups acting on quasi-median graphs. More precisely, we define special actions on quasi-median graphs, and we show that a group which acts specially on a quasi-median graph with finitely many orbits of vertices must embed as a virtual retract into a graph product of finite extensions of clique-stabilizers. In the second part of the article, we apply the theory to fundamental groups of some graphs of groups called right-angled graphs of groups.

Keywords

quasi-median graphsgraph products of groupsspecial cube complexes

MSC classification

Primary: 20F65: Geometric group theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 75 , Issue 3 , June 2023 , pp. 743 - 777
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

This work was supported by a public grant as part of the Fondation Mathématique Jacques Hadamard.

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