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2001 On asymptotic dimension of groups
G Bell, Alexander N Dranishnikov
Algebr. Geom. Topol. 1(1): 57-71 (2001). DOI: 10.2140/agt.2001.1.57

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: asdimACB<.

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<.

Citation

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G Bell. Alexander N Dranishnikov. "On asymptotic dimension of groups." Algebr. Geom. Topol. 1 (1) 57 - 71, 2001. https://doi.org/10.2140/agt.2001.1.57

Information

Received: 11 December 2000; Revised: 12 January 2001; Accepted: 12 January 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 1008.20039
MathSciNet: MR1808331
Digital Object Identifier: 10.2140/agt.2001.1.57

Subjects:
Primary: 20H15
Secondary: 20E34, 20F69

Rights: Copyright © 2001 Mathematical Sciences Publishers

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