N ov 2 00 1 ON ASYMPTOTIC DIMENSION OF GROUPS ACTING ON TREES

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. §0 Introduction The notion of the asymptotic… (More)

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