On asymptotic dimension of groups

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: $asdim A *_{C} B < \infty$ .

B) Suppose that $G^{'}$ is an HNN extension of a group $G$ with $asdim G < \infty$ . Then $asdim G^{'} < \infty$ .

C) Suppose that $Γ$ is Davis’ group constructed from a group $π$ with $asdim π < \infty$ . Then $asdim Γ < \infty$ .

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

Volume 1, issue 1 (2001)

G Bell and A Dranishnikov