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Group actions on injective spaces and Helly graphs

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arxiv 2307.00414 v2 pith:KJMCNVXF submitted 2023-07-01 math.GR math.GTmath.MG

Thomas Haettel This is my paper · ORCID
classification math.GRmath.GTmath.MG
keywords spacesactionsgraphshellyinjectivegroupgroupsmetric
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These are lecture notes for a minicourse on group actions on injective spaces and Helly graphs, given at the CRM Montreal in June 2023. We review the basics of injective metric spaces and Helly graphs, emphasizing the parallel between the two theories. We also describe various elementary properties of groups actions on such spaces. We present several constructions of injective metric spaces and Helly graphs with interesting actions of many groups of geometric nature. We also list a few exercises and open questions at the end.

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  1. New tools in hierarchical hyperbolicity: A survey

    math.GR 2025-07 accept

    A survey of tools for hierarchical hyperbolicity, including combinatorial HHSs, injective metrics, asymptotically CAT(0) metrics, curtains, R-cubings, and higher-rank JSJ decompositions.

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