A note on virtual duality and automorphism groups of right-angled Artin groups
Group Theory
2025-02-21 v2
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.
Keywords
Cite
@article{arxiv.2101.08225,
title = {A note on virtual duality and automorphism groups of right-angled Artin groups},
author = {Richard D. Wade and Benjamin Brück},
journal= {arXiv preprint arXiv:2101.08225},
year = {2025}
}
Comments
11 pages, 3 figures. Article by Wade, with an appendix by Br\"uck. Version accepted to Glasgow Mathematical Journal