Quasi-trees, Lipschitz free spaces, and actions on $\ell^1$

Ignacio Vergara

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arXiv · 2409.14186

Quasi-trees, Lipschitz free spaces, and actions on $\ell^1$

Ignacio Vergara

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Abstract

We show that the Lipschitz free space of a countable simplicial quasi-tree is isomorphic to $\ell^1$. As a consequence, every finitely generated group with Property (QT) of Bestvina--Bromberg--Fujiwara has a proper uniformly Lipschitz affine action on $\ell^1$ with quasi-isometrically embedded orbits. We also show that $3$-manifold groups admit proper uniformly Lipschitz affine actions on $\ell^1$.

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BibTeX RIS

Ignacio Vergara. 2024-09-21. Quasi-trees, Lipschitz free spaces, and actions on $\ell^1$. https://arxiv.org/abs/2409.14186

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