Asymptotic dimension of discrete groups

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 -