Products of free groups inside graph braid groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911838820630528 |
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| author | Jankiewicz, Kasia Schreve, Kevin |
| author_facet | Jankiewicz, Kasia Schreve, Kevin |
| contents | Given a graph $Γ$ and a number $n$, the associated $n^{th}$ graph braid group $B_n(Γ)$ is the fundamental group of the unordered configuration space of $n$ points on $Γ$. Świątkowski showed that for a given $Γ$ and $n$ large enough, there is a free abelian subgroup of $B_n(Γ)$ of rank equal to the cohomological dimension of $B_n(Γ)$. In this note, we observe that at the cost of possibly adding additional points, we can find a subgroup of the same cohomological dimension which is a direct product of non-abelian free groups, and give some applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Products of free groups inside graph braid groups Jankiewicz, Kasia Schreve, Kevin Group Theory Geometric Topology 20F65, 20F36 Given a graph $Γ$ and a number $n$, the associated $n^{th}$ graph braid group $B_n(Γ)$ is the fundamental group of the unordered configuration space of $n$ points on $Γ$. Świątkowski showed that for a given $Γ$ and $n$ large enough, there is a free abelian subgroup of $B_n(Γ)$ of rank equal to the cohomological dimension of $B_n(Γ)$. In this note, we observe that at the cost of possibly adding additional points, we can find a subgroup of the same cohomological dimension which is a direct product of non-abelian free groups, and give some applications. |
| title | Products of free groups inside graph braid groups |
| topic | Group Theory Geometric Topology 20F65, 20F36 |
| url | https://arxiv.org/abs/2404.08863 |