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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.
A. Dranishnikov, and J. Smith. "Asymptotic dimension of discrete groups." Fundamenta Mathematicae 189.1 (2006): 27-34. <http://eudml.org/doc/283232>.
@article{A2006, abstract = {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.}, author = {A. Dranishnikov, J. Smith}, journal = {Fundamenta Mathematicae}, keywords = {asymptotic dimension; solvable groups; Hirsch lengths; quasi-isometry invariants; finitely generated groups; coarse equivalences; word metrics}, language = {eng}, number = {1}, pages = {27-34}, title = {Asymptotic dimension of discrete groups}, url = {http://eudml.org/doc/283232}, volume = {189}, year = {2006}, }
TY - JOUR AU - A. Dranishnikov AU - J. Smith TI - Asymptotic dimension of discrete groups JO - Fundamenta Mathematicae PY - 2006 VL - 189 IS - 1 SP - 27 EP - 34 AB - 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. LA - eng KW - asymptotic dimension; solvable groups; Hirsch lengths; quasi-isometry invariants; finitely generated groups; coarse equivalences; word metrics UR - http://eudml.org/doc/283232 ER -