A note on virtual duality and automorphism groups of right-angled Artin groups
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910835962544128 |
|---|---|
| author | Wade, Richard D. Brück, Benjamin |
| author_facet | Wade, Richard D. Brück, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_08225 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A note on virtual duality and automorphism groups of right-angled Artin groups Wade, Richard D. Brück, Benjamin Group Theory 20E36, 20F36 (Primary) 20J06, 55M05 (Secondary) 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. |
| title | A note on virtual duality and automorphism groups of right-angled Artin groups |
| topic | Group Theory 20E36, 20F36 (Primary) 20J06, 55M05 (Secondary) |
| url | https://arxiv.org/abs/2101.08225 |