Assouad-Nagata dimension of locally finite groups and asymptotic cones

Autor:	Higes, J.
Rok vydání:	2007
Předmět:	Mathematics - Metric Geometry Mathematics - Group Theory Mathematics - Geometric Topology 54F45 (Primary) 55M10 54C65 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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 Comment: 15 pages, added proposition 3.2, corrected misprints and improved some proofs
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0711.1512 Zobrazit plný text záznamu View this record from Arxiv