Group actions on quasi-median graphs and acylindrical hyperbolicity

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• Motiejus Valiunas (Southampton)
• Friday 22 February 2019, 13:45-14:45
• CMS, MR13.

If you have a question about this talk, please contact Richard Webb.

CAT (0) cube complexes form a class of non-positively curved spaces playing a special role in geometric group theory. For instance, such spaces arise naturally in the study of right-angled Artin or Coxeter groups. These complexes can be identified with the class of median graphs, and the latter can be generalised to quasi-median graphs, or ‘CAT (0) prism complexes’. Recent work of A. Genevois has equipped quasi-median graphs with a rich combinatorial structure akin to that of CAT (0) cube complexes, which is useful in studying group actions. In particular, we may use quasi-median graphs to study graph products – a class of groups that interpolate between direct and free products.

In this talk I will give a brief introduction to quasi-median graphs and their cubical-like geometry. I will construct the ‘contact graph’ of a quasi-median graph, which turns out to be quasi-isometric to a tree, and explain the conditions under which a group action on a quasi-median graph induces a particularly nice (acylindrical) action on the contact graph. If time permits, I will outline an application or two to graph products.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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