Dimension invariants of outer automorphism groups

2016/02/13 by Degrijse, Dieter, Souto, Juan
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1602.04354

Abstract

The geometric dimension for proper actions \underlinegd(G) of a group G is the minimal dimension of a classifying space for proper actions \underlineEG. 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 \underlinegd(Γ) but such that the outer automorphism group Out(G) is virtually torsion-free, admits a cocompact model for \underline EOut(G) but nonetheless has vcd(Out(G))≤\underlinegd(Out(G))-r.

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