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Constructing metric spaces from systems of walls (2404.12057v1)

Published 18 Apr 2024 in math.GR and math.MG

Abstract: We give a general procedure for constructing metric spaces from systems of partitions. This generalises and provides analogues of Sageev's construction of dual CAT(0) cube complexes for the settings of hyperbolic and injective metric spaces. As applications, we produce a universal'' hyperbolic action for groups with strongly contracting elements, and show that many groups withcoarsely cubical'' features admit geometric actions on injective metric spaces. In an appendix with Davide Spriano, we show that a large class of groups have an infinite-dimensional space of quasimorphisms.

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