Assouad-Nagata dimension of connected Lie groups

Autor:	Higes, J., Peng, I.
Rok vydání:	2009
Předmět:	Mathematics - Group Theory Mathematics - Differential Geometry Mathematics - Geometric Topology 20F69 (Primary) 22E25 20F16 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages. Main theorem has been extended to connected Lie groups. Added section 6, section 7 and example 4.11
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0910.4569 Zobrazit plný text záznamu View this record from Arxiv