Groups, Geometry, and Dynamics


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Volume 3, Issue 4, 2009, pp. 541–554
DOI: 10.4171/GGD/69

Published online: 2009-12-23

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

Kai-Uwe Bux[1], Ruth Charney[2] and Karen Vogtmann[3]

(1) Universit├Ąt Bielefeld, Germany
(2) Brandeis University, Waltham, USA
(3) University of Warwick, Coventry, United Kingdom

We compute the virtual cohomological dimension 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 $2$-dimensional right-angled Artin group. In the case of a right-angled Artin group with defining graph a tree, the bounds agree.

Keywords: Right-angled Artin groups, symmetric automorphisms

Bux Kai-Uwe, Charney Ruth, Vogtmann Karen: Automorphisms of two-dimensional RAAGS and partially symmetric automorphisms of free groups. Groups Geom. Dyn. 3 (2009), 541-554. doi: 10.4171/GGD/69