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



Autor: J. Higes, I. Peng

Fuente: https://arxiv.org/







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