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 p...

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Bibliographic Details
Published in:arXiv.org 2023-05
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, Br\"uck describes how he used a computer-assisted search to find further examples.
ISSN:2331-8422