On asymptotic dimension of groups acting on trees

Abstract

We prove the following theorem: Let $\pi$ be the fundamental group of a finite graph of groups with finitely generated vertex groups $G_v$ having asdim $G_v\le n$ for all vertices $v$. Then asdim$\pi \le n+1$. This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.

12 pages

References in corpus (1)

• Every Coxeter group acts amenably on a compact space

Cited by in corpus (2)

• Universal spaces for asymptotic dimension
• Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity