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arXiv · 2205.04367

Metric Spaces of Arbitrary Finitely-Generated Scaling Group

Daniel N. Levitin
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Abstract

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 $Γ$.

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Daniel N. Levitin. 2023-06-19. Metric Spaces of Arbitrary Finitely-Generated Scaling Group. https://doi.org/10.1512/iumj.2024.73.9918

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