On Asymptotic Dimension of Groups Acting on Trees

By Gregory C. Bell, Alexander Dranishnikov. 2001

72 citations recorded by the source corpus.

We prove the following.THEOREM. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groupsGv having asdim Gv≤nfor 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/16e978ac8c5afc134a2f8cacd450a6dbccc3955d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Denis V. Osin
2. Alexander Dranishnikov
3. Michael Hull
4. Alessandro Sisto
5. Yves Cornulier

In Geometry and Topology

1. Denis V. Osin
2. M. Zarichnyǐ
3. Alexander Dranishnikov
4. Mark F. Hagen
5. Alessandro Sisto
6. Gregory C. Bell
7. Ashot Minasyan
8. Michael Hull

In Mathematical Physics

1. Denis V. Osin
2. M. Zarichnyǐ
3. Alexander Dranishnikov
4. Mark F. Hagen
5. E. Guentner
6. Gregory C. Bell
7. Alessandro Sisto
8. Michael Hull

Citations in the corpus

• Asymptotic dimension of relatively hyperbolic groups (2004, background): “And again asdimG < ∞ whenever asdimH < ∞ [2].”
• Universal spaces for asymptotic dimension (2002, background): “results are of a particular interest. In [14] Gromov proved that all the hyperbolic groups have finite asymptotic dimension. In [11] the finite dimensionality was established for all Coxeter groups. In [2, 3] finite dimensionality theorems were proved for the fundamental group of graphs of groups. In p”