A note on virtual duality and automorphism groups of right-angled Artin groups

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 pa...

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Bibliographic Details
Published in:Glasgow mathematical journal 2023-09, Vol.65 (3), p.573-581
Main Authors: Wade, Richard D., Brück, Benjamin
Format: Article
Language:English
Subjects:
Automorphisms
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Summary: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.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089523000149