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arXiv · 2010.03709

Asymptotic and Assouad-Nagata dimension of finitely generated groups and their subgroups

Levi Sledd
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Abstract

We prove that for all $k,m,n \in \mathbb N \cup \{\infty\}$ with $4 \leq k \leq m \leq n$, there exists a finitely generated group $G$ with a finitely generated subgroup $H$ such that the asymptotic dimension of $G$ is $k$, the Assouad-Nagata dimension of $G$ is $m$, and the Assouad-Nagata dimension of $H$ is $n$. This simultaneously answers two open questions in asymptotic dimension theory.

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Levi Sledd. 2020-10-08. Asymptotic and Assouad-Nagata dimension of finitely generated groups and their subgroups. https://arxiv.org/abs/2010.03709

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