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.
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Bell, G., Dranishnikov, A. On Asymptotic Dimension of Groups Acting on Trees. Geometriae Dedicata 103, 89–101 (2004). https://doi.org/10.1023/B:GEOM.0000013843.53884.77
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DOI: https://doi.org/10.1023/B:GEOM.0000013843.53884.77