Volume 1, issue 1 (2001)

Download this article
For printing
Recent Issues

Volume 22
Issue 8, 3533–4008
Issue 7, 3059–3532
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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
References
Forward citations
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