Algorithmic verification of quasi-isometry of some HNN-extensions of Abelian groups.
Asymptotic dimension of coarse spaces.
Asymptotic dimension of discrete groups
We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for the asymptotic dimension of finitely generated solvable groups in terms of their Hirsch length.
Asymptotic dimension of one relator groups
We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov, and we give an improved estimate of that dimension in terms of the relator length. The construction is similar to one of Bell and Dranishnikov, but we produce a sharper estimate.