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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Cambridge University Press
2023
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| _version_ | 1797112000156794880 |
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| author | Wade, RD Brück, B |
| author_facet | Wade, RD Brück, B |
| author_sort | Wade, RD |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T08:18:13Z |
| format | Journal article |
| id | oxford-uuid:1e991a3f-ff43-48af-b7a1-50e569798ca7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:18:13Z |
| publishDate | 2023 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:1e991a3f-ff43-48af-b7a1-50e569798ca72024-01-17T13:31:02ZA note on virtual duality and automorphism groups of right-angled Artin groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1e991a3f-ff43-48af-b7a1-50e569798ca7EnglishSymplectic ElementsCambridge University Press2023Wade, RDBrück, BA 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. |
| spellingShingle | Wade, RD Brück, B A note on virtual duality and automorphism groups of right-angled Artin groups |
| title | A note on virtual duality and automorphism groups of right-angled Artin groups |
| title_full | A note on virtual duality and automorphism groups of right-angled Artin groups |
| title_fullStr | A note on virtual duality and automorphism groups of right-angled Artin groups |
| title_full_unstemmed | A note on virtual duality and automorphism groups of right-angled Artin groups |
| title_short | A note on virtual duality and automorphism groups of right-angled Artin groups |
| title_sort | note on virtual duality and automorphism groups of right angled artin groups |
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