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On asymptotic dimension of groups

G Bell and A Dranishnikov

Algebraic & Geometric Topology 1 (2001) 57–71

arXiv: math.GR/0012006

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: asdimA CB < .

B) Suppose that G is an HNN extension of a group G with asdimG < . Then asdimG < .

C) Suppose that Γ is Davis’ group constructed from a group π with asdimπ < . Then asdimΓ < .

Keywords
Asymptotic dimension, amalgamated product, HNN extension
Mathematical Subject Classification 2000
Primary: 20H15
Secondary: 20E34, 20F69
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Publication
Received: 11 December 2000
Revised: 12 January 2001
Accepted: 12 January 2001
Published: 27 January 2001
Authors
G Bell
University of Florida
Department of Mathematics
PO Box 118105
358 Little Hall
Gainesville FL 32611-8105
USA
A Dranishnikov
University of Florida
Department of Mathematics
PO Box 118105
358 Little Hall
Gainesville FL 32611-8105
USA