On asymptotic dimension of amalgamated products and right-angled Coxeter groups

Dranishnikov, Alexander N

doi:10.2140/agt.2008.8.1281

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On asymptotic dimension of amalgamated products and right-angled Coxeter groups

Alexander Dranishnikov

Algebraic & Geometric Topology 8 (2008) 1281–1293

DOI: 10.2140/agt.2008.8.1281

Abstract

We prove that the asymptotic dimension of $A$ and $B$ amalgamated over $C$ is bounded above by the maximum of the asymptotic dimensions of $A$ , $B$ and $C + 1$ . Then we apply this inequality to show that the asymptotic dimension of any right-angled Coxeter group does not exceed the dimension of its Davis complex.

Keywords

asymptotic dimension, amalgamated product, Coxeter group

Mathematical Subject Classification 2000

Primary: 20F65, 20F55, 20F69

References

Publication

Received: 17 May 2007

Revised: 13 February 2008

Accepted: 13 February 2008

Published: 8 August 2008

Authors

Alexander Dranishnikov
University of Florida Department of Mathematics PO Box 118105 358 Little Hall Gainesville, FL 32611-8105 USA
http://www.math.ufl.edu/~dranish

Volume 8, issue 3 (2008)