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Actions on products of \(\textrm{CAT}(-1)\) spaces

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Abstract

We show that for X a proper \(\textrm{CAT}(-1)\) space there is a maximal open subset of the horofunction compactification of \(X\times X\), with respect to the maximum metric, that compactifies the diagonal action of an infinite quasi-convex group of the isometries of X. We also consider the product action of two quasi-convex representations of an infinite hyperbolic group on the product of two different proper \(\textrm{CAT}(-1)\) spaces.

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Acknowledgements

We are indebted to the anonymous referee for suggestions that have improved substantially the paper.

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Authors and Affiliations

  1. Departament de Matemàtiques, Centre de Recerca Matemàtica (CRM), Universitat Autònoma de Barcelona, 08193, Cerdanyola del Vallès, Spain

    Teresa García & Joan Porti

  2. Centre de Recerca Matemàtica (CRM), 08193 , Cerdanyola del Vallés, Spain

    Teresa García & Joan Porti

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  1. Teresa García
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  2. Joan Porti
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Correspondence to Joan Porti.

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Teresa García supported by Grant BES-2013-065701 and Joan Porti by María de Maeztu Program for Centers and Units of Excellence (CEX2020-001084-M). Both authors partially supported by Grant FEDER-Meic MTM2015-66165-P.

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García, T., Porti, J. Actions on products of \(\textrm{CAT}(-1)\) spaces. Geom Dedicata 217, 69 (2023). https://doi.org/10.1007/s10711-023-00805-y

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