On asymptotic dimension of groups acting on trees

الأصل · EN

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