Assouad-Nagata dimension of locally finite groups and asymptotic cones

Details Assouad-Nagata dimension of locally finite groups and asymptotic cones Assouad-Nagata dimension of locally finite groups and asymptotic cones

2007-11-09

arxiv.org/abs/0711.1512v3

Mathematics

Metric Geometry

15 pages, added proposition 3.2, corrected misprints and improved some proofs

Scientific paper

In this work we study two problems about Assouad-Nagata dimension: 1) Is there a metric space of non zero Assouad-Nagata dimension such that all of its asymptotic cones are of Assouad-Nagata dimension zero? (Dydak and Higes) 2) Suppose $G$ is a locally finite group with a proper left invariant metric $d_G$. If $\dim_{AN}(G, d_G)>0$, is $\dim_{AN} (G, d_G)$ infinite?(Brodskiy, Dydak and Lang) The first question is answered positively not only for general metric spaces but also for discrete groups with proper left invariant metrics. The second question has a negative solution. We show that for each $n$ there exists a locally finite group of Assouad-Nagata dimension $n$. A generalization to countable groups of arbitrary asymptotic dimension is given

Affiliated with

Also associated with

No associations

Rating

Assouad-Nagata dimension of locally finite groups and asymptotic cones 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 locally finite groups and asymptotic cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Assouad-Nagata dimension of locally finite groups and asymptotic cones will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-702768