Classifying spaces for families of virtually abelian subgroups of surface braid groups
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arXiv
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| Format: | Preprint |
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2026
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| author | Flores, Ramón González-Meneses, Juan León-Álvarez, Porfirio L. |
| author_facet | Flores, Ramón González-Meneses, Juan León-Álvarez, Porfirio L. |
| contents | Given a group $G$ and an integer $n \geq 0$, let $\mathcal{F}_n$ denote the family of all virtually abelian subgroups of $G$ of rank at most $n$. In this article, we show that for each $n \geq 1$, the minimal dimension of a model for the classifying space $E_{\mathcal{F}_n}G$ for the pure braid group of a surface of non-negative Euler characteristic with at least one boundary component or one puncture is equal to the virtual cohomological dimension of $G$ plus $n$. We prove an analogous result for the full braid group of the sphere. As an application, we compute the minimal dimension of a model for the classifying space associated to the family of amenable subgroups of pure surface braid groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classifying spaces for families of virtually abelian subgroups of surface braid groups Flores, Ramón González-Meneses, Juan León-Álvarez, Porfirio L. Group Theory Algebraic Topology Geometric Topology 20F36 Given a group $G$ and an integer $n \geq 0$, let $\mathcal{F}_n$ denote the family of all virtually abelian subgroups of $G$ of rank at most $n$. In this article, we show that for each $n \geq 1$, the minimal dimension of a model for the classifying space $E_{\mathcal{F}_n}G$ for the pure braid group of a surface of non-negative Euler characteristic with at least one boundary component or one puncture is equal to the virtual cohomological dimension of $G$ plus $n$. We prove an analogous result for the full braid group of the sphere. As an application, we compute the minimal dimension of a model for the classifying space associated to the family of amenable subgroups of pure surface braid groups. |
| title | Classifying spaces for families of virtually abelian subgroups of surface braid groups |
| topic | Group Theory Algebraic Topology Geometric Topology 20F36 |
| url | https://arxiv.org/abs/2604.15243 |