A note on finiteness properties of vertex stabilisers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917931065016320 |
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| author | Li, Kevin Saldaña, Luis Jorge Sánchez |
| author_facet | Li, Kevin Saldaña, Luis Jorge Sánchez |
| contents | We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of $G$-CW-complexes, given the finiteness properties of the group $G$ and of the stabilisers of positive dimensional cells. This generalises a result of Haglund--Wise for groups acting on trees to higher dimensions. As an application, for $n\ge 2$, we deduce the existence of uncountably many quasi-isometry classes of one-ended groups that are of type $\mathsf{FP}_n$ and not of type $\mathsf{FP}_{n+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on finiteness properties of vertex stabilisers Li, Kevin Saldaña, Luis Jorge Sánchez Group Theory 20J05, 57M07, 20F65 We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of $G$-CW-complexes, given the finiteness properties of the group $G$ and of the stabilisers of positive dimensional cells. This generalises a result of Haglund--Wise for groups acting on trees to higher dimensions. As an application, for $n\ge 2$, we deduce the existence of uncountably many quasi-isometry classes of one-ended groups that are of type $\mathsf{FP}_n$ and not of type $\mathsf{FP}_{n+1}$. |
| title | A note on finiteness properties of vertex stabilisers |
| topic | Group Theory 20J05, 57M07, 20F65 |
| url | https://arxiv.org/abs/2502.14751 |