On the Recognition of Right-Angled Artin Groups

Bridson, Martin R.

doi:10.1017/s0017089519000235

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Cited by 2 publications

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“…However, the Join Lemma does provide a way to construct families of examples that are finite index in for some (and now the work of Wiedmer greatly extends this [29]). It is also worth noting that [16, Question 1.2] gave a more general recognition problem about RAAGs, which was later answered in the negative by Bridson [10].…”

Section: Further Discussionmentioning

confidence: 99%

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

Wade

Brück

2023

Glasgow Math. J.

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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.

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Section: Further Discussionmentioning

confidence: 99%

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

Wade

Brück

2023

Glasgow Math. J.

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show abstract

“…However, the Join Lemma does provide a way to construct families of examples A ∆ that are finite index in Out(A Γ ) for some Γ. It is also worth noting that [16,Question 1.2] gave a more general recognition problem about RAAGs, which was later answered in the negative by Bridson [10].…”

Section: Commensurability Problemsmentioning

confidence: 99%

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

Wade¹,

Brück²

2021

Preprint

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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.

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On the Recognition of Right-Angled Artin Groups

Abstract: There does not exist an algorithm that can determine whether or not a group presented by commutators is a right-angled Artin group.1991 Mathematics Subject Classification. 20F36, 20F10.

Cited by 2 publications

References 7 publications

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

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

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

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