descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 27 Jan 2001Embargo end date: 01 Jan 2000 English Publisher:Mathematical Sciences PublishersJournal:Algebraic & Geometric Topology, volume 1, pages 57-71 (issn: 1472-2747, eissn: 1472-2739,

Authors: Bell, G; Dranishnikov, Alexander N;

doi: 10.2140/agt.2001.1.57 , 10.48550/arxiv.math/0012006

arXiv: http://arxiv.org/abs/math/0012006

On asymptotic dimension of groups

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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 ��is Davis' group constructed from a group ��with asdim��< infinity. Then asdim��< infinity.

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

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University of Florida
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Keywords

20H15, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Extensions, wreath products, and other compositions of groups, Group Theory (math.GR), 20H15, 20E34, 20F69, finitely generated groups, HNN extensions, groups acting on trees, Mathematics - Geometric Topology, free products, Fundamental groups and their automorphisms (group-theoretic aspects), FOS: Mathematics, Generators, relations, and presentations of groups, asymptotic dimension, 20F69, Geometric Topology (math.GT), amalgamated products, HNN extension, amalgamated product, Asymptotic properties of groups, Groups acting on trees, Asymptotic dimension, 20E34, Mathematics - Group Theory

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