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arXiv · 0910.4569

Assouad-Nagata dimension of connected Lie groups

J. Higes·I. Peng
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Abstract

We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group $G$ equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C$ where $C$ is a maximal compact subgroup. To prove it we will compute the Assouad-Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad-Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometric to any cocompact lattice on a connected Lie group.

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BibTeXRIS

J. Higes, I. Peng. 2009-10-23. Assouad-Nagata dimension of connected Lie groups. https://arxiv.org/abs/0910.4569

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