Geometriae Dedicata

, Volume 103, Issue 1, pp 89–101

On Asymptotic Dimension of Groups Acting on Trees


  • G. Bell
    • Department of MathematicsUniversity of Louisville
  • A. Dranishnikov
    • Department of MathematicsUniversity of Florida

DOI: 10.1023/B:GEOM.0000013843.53884.77

Cite this article as:
Bell, G. & Dranishnikov, A. Geometriae Dedicata (2004) 103: 89. doi:10.1023/B:GEOM.0000013843.53884.77


We prove the following.

THEOREM. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groupsGv having asdim Gvnfor 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.

amalgamated free productasymptotic dimensiongraph of groupsHNN extension

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© Kluwer Academic Publishers 2004