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arXiv · 2207.14691

Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$

Ignacio Vergara
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Abstract

We show that every hyperbolic group has a proper uniformly Lipschitz affine action on a subspace of an $L^1$ space. We also prove that every acylindrically hyperbolic group has a uniformly Lipschitz affine action on such a space with unbounded orbits. Our main tools are the $\mathbb{Q}$-bicombings on hyperbolic groups constructed by Mineyev and the characterisation of acylindrical hyperbolicity in terms of actions on quasi-trees by Balasubramanya.

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Ignacio Vergara. 2022-07-29. Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$. https://doi.org/10.1112/blms.12873

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