Geodesic
Acylindrical hyperbolicity of groups acting on quasi-median graphs and equations in graph products
Motiejus Valiunas1
1University of Wroclaw, Poland
Groups, geometry, and dynamics, Tome 15 (2021) no. 1, pp. 143-195

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DOI

In this paper we study group actions on quasi-median graphs, or "CAT(0) prism complexes", generalising the notion of CAT(0) cube complexes. We consider hyperplanes in a quasi-median graph X and define the contact graph CX for these hyperplanes. We show that CX is always quasi-isometric to a tree, generalising a result of Hagen [18], and that under certain conditions a group action G↷X induces an acylindrical action G↷CX, giving a quasi-median analogue of a result of Behrstock, Hagen and Sisto [5].
DOI : 10.4171/ggd/595
Classification : 20-XX
Mots-clés : Acylindrically hyperbolic groups, equationally noetherian groups, graph products, quasi-median graphs

Motiejus Valiunas  1

1 University of Wroclaw, Poland 
Motiejus Valiunas. Acylindrical hyperbolicity of groups acting on quasi-median graphs and equations in graph products. Groups, geometry, and dynamics, Tome 15 (2021) no. 1, pp. 143-195. doi: 10.4171/ggd/595
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