The geometric dimension for proper actions gd(G) of a group G is the minimal dimension of a classifying space for proper actions EG. We construct for every integer r≥1, an example of a virtually torsion-free Gromov-hyperbolic group G such that for every group Γ which contains G as a finite index normal subgroup, the virtual cohomological dimension vcd(Γ) of Γ equals gd(Γ) but such that the outer automorphism group Out(G) is virtually torsion-free, admits a cocompact model for E Out(G) but nonetheless has vcd(Out(G))≤gd(Out(G))−r.
1
National University of Ireland, Galway, Ireland
2
Université de Rennes 1, France
Dieter Degrijse; Juan Souto. Dimension invariants of outer automorphism groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1469-1495. doi: 10.4171/ggd/435
@article{10_4171_ggd_435,
author = {Dieter Degrijse and Juan Souto},
title = {Dimension invariants of outer automorphism groups},
journal = {Groups, geometry, and dynamics},
pages = {1469--1495},
year = {2017},
volume = {11},
number = {4},
doi = {10.4171/ggd/435},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/435/}
}
TY - JOUR
AU - Dieter Degrijse
AU - Juan Souto
TI - Dimension invariants of outer automorphism groups
JO - Groups, geometry, and dynamics
PY - 2017
SP - 1469
EP - 1495
VL - 11
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/435/
DO - 10.4171/ggd/435
ID - 10_4171_ggd_435
ER -
%0 Journal Article
%A Dieter Degrijse
%A Juan Souto
%T Dimension invariants of outer automorphism groups
%J Groups, geometry, and dynamics
%D 2017
%P 1469-1495
%V 11
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/435/
%R 10.4171/ggd/435
%F 10_4171_ggd_435
