Assouad-Nagata dimension of connected Lie groups

Details Assouad-Nagata dimension of connected Lie groups Assouad-Nagata dimension of connected Lie groups

2009-10-23

arxiv.org/abs/0910.4569v3

Mathematics

Group Theory

21 pages. Main theorem has been extended to connected Lie groups. Added section 6, section 7 and example 4.11

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Assouad-Nagata dimension of connected Lie groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Assouad-Nagata dimension of connected Lie groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Assouad-Nagata dimension of connected Lie groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-424134