On asymptotic dimension of groups

Details On asymptotic dimension of groups On asymptotic dimension of groups

2000-12-02

arxiv.org/abs/math/0012006v2

Algebraic and Geometric Topology 1 (2001) 57-71

Mathematics

Group Theory

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-4.abs.html

Scientific paper

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.

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