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 inGlasgow mathematical journal Vol. 65; no. 3; pp. 573 - 581
Main Authors Wade, Richard D., Brück, Benjamin
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2023
Subjects
Automorphisms
20J06
duality groups
55M05
Right-angled Artin groups
20F36
automorphisms
20E36
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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