Volume 8, issue 3 (2008)

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

Alexander Dranishnikov

Algebraic & Geometric Topology 8 (2008) 1281–1293
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