, Volume 103, Issue 1, pp 89-101

On Asymptotic Dimension of Groups Acting on Trees

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Abstract

We prove the following.

THEOREM. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groups G v having asdim G v n for all vertices v. Then asdim π≤n+1.

This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.