Automorphisms of two-dimensional RAAGs and partially symmetric automorphisms of free groups

2008/04/15 by Bux, Kai-Uwe, Charney, Ruth, Vogtmann, Karen
#20F36 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0804.2300

Abstract

We compute the virtual cohomological dimension (VCD) of the group of partially symmetric outer automorphisms of a free group. We use this to obtain new upper and lower bounds on the VCD of the outer automorphism group of a two-dimensional right-angled Artin group. In the case of a right-angled group with defining graph a tree, the bounds agree.

Related

• Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisations
• Realising VCD for untwisted automorphism groups of RAAGs
• Automorphisms of higher-dimensional right-angled Artin groups
• Relative outer automorphisms of free groups
• Dimension invariants of outer automorphism groups