Relative outer automorphisms of free groups

2010/10/22 by Meucci, Erika
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1010.4753

Abstract

Let A₁,...,A_k be a system of free factors of F_n. The group of relative automorphisms Aut(F_n;A₁,...,A_k) is the group given by the automorphisms of F_n that restricted to each A_i are conjugations by elements in F_n. The group of relative outer automorphisms is defined as Out(F_n;A₁,...,A_k) = Aut(F_n;A₁,...,A_k)/Inn(F_n), where Inn(F_n) is the normal subgroup of Aut(F_n) given by all the inner automorphisms. We define a contractible space on which Out(F_n;A₁,...,A_k) acts with finite stabilizers and we compute the virtual cohomological dimension of this group.

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