Assouad-Nagata dimension of connected Lie groups - Mathematics > Group TheoryReport as inadecuate




Assouad-Nagata dimension of connected Lie groups - Mathematics > Group Theory - Download this document for free, or read online. Document in PDF available to download.

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.



Author: J. Higes, I. Peng

Source: https://arxiv.org/







Related documents