Bogomolov multipliers of word labelled oriented graph groups
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912332455608320 |
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| author | Roy, Mallika |
| author_facet | Roy, Mallika |
| contents | A group, whose presentation is explicitly derived in a certain way from a word labelled oriented graph (in short, WLOG), is called a WLOG group. In this work, we study homological version of Bogomolov multiplier (denoted by $\widetilde{B_0}$) for this family of groups. We prove how to compute the generators for the $\widetilde{B_0}(G)$ of a WLOG group $G$ from the underlying WLOG. We exhibit finitely presented Bestvina--Brady groups and Artin groups as WLOG groups. As applications, we compute both the multipliers: the homological version of Bogomolov multipliers and Schur multipliers, of these groups utilizing their respective WLOG group presentations. Our computation gives a new proof of the structure of the Schur multiplier of a finitely presented Bestvina--Brady group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bogomolov multipliers of word labelled oriented graph groups Roy, Mallika Group Theory 20E05, 20F05, 20F67 A group, whose presentation is explicitly derived in a certain way from a word labelled oriented graph (in short, WLOG), is called a WLOG group. In this work, we study homological version of Bogomolov multiplier (denoted by $\widetilde{B_0}$) for this family of groups. We prove how to compute the generators for the $\widetilde{B_0}(G)$ of a WLOG group $G$ from the underlying WLOG. We exhibit finitely presented Bestvina--Brady groups and Artin groups as WLOG groups. As applications, we compute both the multipliers: the homological version of Bogomolov multipliers and Schur multipliers, of these groups utilizing their respective WLOG group presentations. Our computation gives a new proof of the structure of the Schur multiplier of a finitely presented Bestvina--Brady group. |
| title | Bogomolov multipliers of word labelled oriented graph groups |
| topic | Group Theory 20E05, 20F05, 20F67 |
| url | https://arxiv.org/abs/2504.12409 |