On asymptotic dimension of groups
Group Theory
2014-10-01 v2 Geometric Topology
Abstract
We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdim A *_C B < infinity. B) Suppose that G' is an HNN extension of a group G with asdim G < infinity. Then asdim G'< infinity. C) Suppose that \Gamma is Davis' group constructed from a group \pi with asdim\pi < infinity. Then asdim\Gamma < infinity.
Cite
@article{arxiv.math/0012006,
title = {On asymptotic dimension of groups},
author = {G. Bell and A. Dranishnikov},
journal= {arXiv preprint arXiv:math/0012006},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-4.abs.html