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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.14186 |
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| _version_ | 1866916405683683328 |
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| author | Vergara, Ignacio |
| author_facet | Vergara, Ignacio |
| contents | 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 $\ell^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-trees, Lipschitz free spaces, and actions on $\ell^1$ Vergara, Ignacio Group Theory Functional Analysis 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 $\ell^1$. |
| title | Quasi-trees, Lipschitz free spaces, and actions on $\ell^1$ |
| topic | Group Theory Functional Analysis |
| url | https://arxiv.org/abs/2409.14186 |