A note on virtual duality and automorphism groups of right-angled Artin groups
Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 573-581
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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.
Mots-clés :
Right-angled Artin groups, automorphisms, duality groups
Wade, Richard D.; Brück, Benjamin. A note on virtual duality and automorphism groups of right-angled Artin groups. Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 573-581. doi: 10.1017/S0017089523000149
@article{10_1017_S0017089523000149,
author = {Wade, Richard D. and Br\"uck, Benjamin},
title = {A note on virtual duality and automorphism groups of right-angled {Artin} groups},
journal = {Glasgow mathematical journal},
pages = {573--581},
year = {2023},
volume = {65},
number = {3},
doi = {10.1017/S0017089523000149},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000149/}
}
TY - JOUR AU - Wade, Richard D. AU - Brück, Benjamin TI - A note on virtual duality and automorphism groups of right-angled Artin groups JO - Glasgow mathematical journal PY - 2023 SP - 573 EP - 581 VL - 65 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000149/ DO - 10.1017/S0017089523000149 ID - 10_1017_S0017089523000149 ER -
%0 Journal Article %A Wade, Richard D. %A Brück, Benjamin %T A note on virtual duality and automorphism groups of right-angled Artin groups %J Glasgow mathematical journal %D 2023 %P 573-581 %V 65 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000149/ %R 10.1017/S0017089523000149 %F 10_1017_S0017089523000149
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