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arXiv · 2101.08225

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

Richard D. Wade·Benjamin Brück
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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, Br\"uck describes how he used a computer-assisted search to find further examples.

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Richard D. Wade, Benjamin Brück. 2021-01-20. A note on virtual duality and automorphism groups of right-angled Artin groups. https://doi.org/10.1017/s0017089523000149

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