JournalsggdVol. 11, No. 4pp. 1469–1495

Dimension invariants of outer automorphism groups

  • Dieter Degrijse

    National University of Ireland, Galway, Ireland
  • Juan Souto

    Université de Rennes 1, France
Dimension invariants of outer automorphism groups cover

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Abstract

The geometric dimension for proper actions gd(G)\underline{\mathrm{gd}}(G) of a group GG is the minimal dimension of a classifying space for proper actions EG\underline{E}G. We construct for every integer r1r\geq 1, an example of a virtually torsion-free Gromov-hyperbolic group GG such that for every group Γ\Gamma which contains GG as a finite index normal subgroup, the virtual cohomological dimension vcd(Γ)(\Gamma) of Γ\Gamma equals gd(Γ)\underline{\mathrm{gd}}(\Gamma) but such that the outer automorphism group Out(G)(G) is virtually torsion-free, admits a cocompact model for E\underline{E} Out(G)(G) but nonetheless has vcd(Out(G))gd(G))\le \underline{\mathrm{gd}}(Out(G))r(G))-r.

Cite this article

Dieter Degrijse, Juan Souto, Dimension invariants of outer automorphism groups. Groups Geom. Dyn. 11 (2017), no. 4, pp. 1469–1495

DOI 10.4171/GGD/435