Metric Spaces of Arbitrary Finitely-Generated Scaling Group
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910746034569216 |
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| author | Levitin, Daniel N. |
| author_facet | Levitin, Daniel N. |
| contents | For a metric space $X$ with a compatible measure $μ$, Genevois and Tessera defined the Scaling Group of $(X,μ)$ as the subgroup $Γ$ of $\mathbb{R}_{>0}$ of positive real numbers $γ$ for which there are quasi-isometries of $X$ coarsely scaling $μ$ by a factor of $γ$. We show that for any finitely generated subgroup $Γ$ of $\mathbb{R}_{>0}$ there exists a space $N_Γ$, bi-Lipschitz equivalent to a graph of finite degree, with scaling group $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04367 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Metric Spaces of Arbitrary Finitely-Generated Scaling Group Levitin, Daniel N. Metric Geometry Group Theory 51F30 (Primary) 20F65 (Secondary) For a metric space $X$ with a compatible measure $μ$, Genevois and Tessera defined the Scaling Group of $(X,μ)$ as the subgroup $Γ$ of $\mathbb{R}_{>0}$ of positive real numbers $γ$ for which there are quasi-isometries of $X$ coarsely scaling $μ$ by a factor of $γ$. We show that for any finitely generated subgroup $Γ$ of $\mathbb{R}_{>0}$ there exists a space $N_Γ$, bi-Lipschitz equivalent to a graph of finite degree, with scaling group $Γ$. |
| title | Metric Spaces of Arbitrary Finitely-Generated Scaling Group |
| topic | Metric Geometry Group Theory 51F30 (Primary) 20F65 (Secondary) |
| url | https://arxiv.org/abs/2205.04367 |