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Dimension invariants of outer automorphism groups

Degrijse, Dieter
; 
Souto, Juan
Repository DOI
Publication Date
2017-12-07
Keywords
outer automorphism groups, geometric dimension for proper actions, virtual cohomological dimension, virtually cyclic subgroups, geometric dimension, classifying-spaces, coxeter groups, family
Type
Article
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Citation
Degrijse, Dieter; Souto, Juan (2017). Dimension invariants of outer automorphism groups. Groups, Geometry, and Dynamics 11 (4), 1469-1495
Abstract
The geometric dimension for proper actions (gd) under bar (G) of a group G is the minimal dimension of a classifying space for proper actions (gd) under barG. We construct for every integer r >= 1, an example of a virtually torsion- free Gromov-hyperbolicgroup G such that for every group. which contains G as a finite index normal sub group, the virtual cohomological dimension vcd(Gamma) of Gamma equals (gd) under bar(Gamma) but such that the outer automorphism group Out(G) is virtually torsion- free, admits a cocompact model for (gd) under bar Out(G) but nonetheless has vcd(Out)(G)) <= gd(Out)(G)) - r.
Funder
Publisher
European Mathematical Publishing House
Publisher DOI
10.4171/ggd/435
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)