A graphical description of the BNS-invariants of Bestvina-Brady groups and the RAAG recognition problem
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912299598479360 |
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| author | Chang, Yu-Chan Ruffoni, Lorenzo |
| author_facet | Chang, Yu-Chan Ruffoni, Lorenzo |
| contents | A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an application, we obtain that the class of BBGs contains the class of RAAGs. On the other hand, we provide a criterion to certify that certain finitely presented BBGs are not isomorphic to RAAGs (or more general Artin groups). This is based on a description of the Bieri-Neumann-Strebel invariants of finitely presented BBGs in terms of separating subgraphs, analogous to the case of RAAGs. As an application, we characterize when the BBG associated to a 2-dimensional flag complex is a RAAG in terms of certain subgraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06901 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A graphical description of the BNS-invariants of Bestvina-Brady groups and the RAAG recognition problem Chang, Yu-Chan Ruffoni, Lorenzo Group Theory Combinatorics Geometric Topology 20F36, 20J05, 20F65, 20F05 A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an application, we obtain that the class of BBGs contains the class of RAAGs. On the other hand, we provide a criterion to certify that certain finitely presented BBGs are not isomorphic to RAAGs (or more general Artin groups). This is based on a description of the Bieri-Neumann-Strebel invariants of finitely presented BBGs in terms of separating subgraphs, analogous to the case of RAAGs. As an application, we characterize when the BBG associated to a 2-dimensional flag complex is a RAAG in terms of certain subgraphs. |
| title | A graphical description of the BNS-invariants of Bestvina-Brady groups and the RAAG recognition problem |
| topic | Group Theory Combinatorics Geometric Topology 20F36, 20J05, 20F65, 20F05 |
| url | https://arxiv.org/abs/2212.06901 |