Centralisers and the virtually cyclic dimension of $\mathrm{Out}(F_N)$
Résumé
We prove that the virtually cyclic (geometric) dimension of the finite index congruence subgroup $\mathrm{IA}_N(3)$ of $\mathrm{Out}(F_N)$ is $2N-2$. From this we deduce the virtually cyclic dimension of $\mathrm{Out}(F_N)$ is finite. Along the way we prove Lück's property (C) holds for $\mathrm{Out}(F_N)$, we prove that the commensurator of a cyclic subgroup of $\mathrm{IA}_N(3)$ equals its centraliser, we give an $\mathrm{IA}_N(3)$ analogue of various exact sequences arising from reduction systems for mapping class groups, and give a near complete description of centralisers of infinite order elements in $\mathrm{IA}_3(3)$.
Mots clés
Outer automorphisms of free groups virtually cyclic dimension classifying spaces centralisers of abelian subgroups
Outer automorphisms of free groups
virtually cyclic dimension
classifying spaces
centralisers of abelian subgroups
Group Theory (math.GR)
Algebraic Topology (math.AT)
Geometric Topology (math.GT)
FOS: Mathematics
20E36
20F28
20F65
55R35
57M07
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)