A note on virtual duality and automorphism groups of right-angled Artin groups
arXiv:2101.08225 · doi:10.1017/s0017089523000149
Abstract
A theorem of Brady and Meier states that a right-angled Artin group is a duality group if and only if the flag complex of the defining graph is Cohen--Macaulay. We use this to give an example of a RAAG with the property that its outer automorphism group is not a virtual duality group. This gives a partial answer to a question of Vogtmann. In an appendix, Brück describes how he used a computer-assisted search to find further examples.
11 pages, 3 figures. Article by Wade, with an appendix by Brück. Version accepted to Glasgow Mathematical Journal
References in corpus (5)
- Relative automorphism groups of right-angled Artin groups
- Quasi-isometry classification of RAAGs that split over cyclic subgroups
- On the bordification of outer space
- Calculating the virtual cohomological dimension of the automorphism group of a RAAG
- Between buildings and free factor complexes: A Cohen-Macaulay complex for Out(RAAGs)