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

TL;DR

This paper establishes an inequality relating the asymptotic dimension of amalgamated products and applies it to show that right-angled Coxeter groups have asymptotic dimension bounded by the dimension of their Davis complex.

Contribution

It proves a new inequality for asymptotic dimensions of amalgamated products and applies it to right-angled Coxeter groups, linking algebraic and geometric properties.

Findings

Proves the inequality *CB  ,,+1.

Shows asymptotic dimension of right-angled Coxeter groups is bounded by the Davis complex dimension.

Provides tools for analyzing asymptotic dimensions in geometric group theory.

Abstract

We prove the inequality $$ \as A\ast_CB\le\max\{\as A,\as B,\as C+1\} $$ and 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.