On asymptotic dimension of groups acting on trees

Abstract

We prove the following theorem: Let $\ddot{I}€$ 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$\ddot{I}€\le n+1$. This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.

12 pages