On asymptotic dimension of groups acting on trees

Details On asymptotic dimension of groups acting on trees On asymptotic dimension of groups acting on trees

2001-11-07

arxiv.org/abs/math/0111087v2

Mathematics

Group Theory

12 pages

Scientific paper

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.

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