Manifold models for hyperbolic graph braid groups on three strands
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910045977968640 |
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| author | Jain, Saumya Vo, Huong |
| author_facet | Jain, Saumya Vo, Huong |
| contents | Given a finite graph $Γ$, the associated graph braid group $B_n(Γ)$ is the fundamental group of the unordered $n$-point configuration space of $Γ$. Genevois classified which graph braid groups are Gromov hyperbolic and asked the question: When do these groups arise as $3$-manifold groups? In this paper, we give a partial answer for $B_3(Θ_m)$, where $Θ_m$ is the generalized $Θ$-graph, a suspension of $m$-points. We show that $B_3(Θ_5)$ is a $3$-manifold group while $B_3(Θ_m)$ is not even quasi-isometric to a $3$-manifold group for $m \geq 7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Manifold models for hyperbolic graph braid groups on three strands Jain, Saumya Vo, Huong Geometric Topology Group Theory Given a finite graph $Γ$, the associated graph braid group $B_n(Γ)$ is the fundamental group of the unordered $n$-point configuration space of $Γ$. Genevois classified which graph braid groups are Gromov hyperbolic and asked the question: When do these groups arise as $3$-manifold groups? In this paper, we give a partial answer for $B_3(Θ_m)$, where $Θ_m$ is the generalized $Θ$-graph, a suspension of $m$-points. We show that $B_3(Θ_5)$ is a $3$-manifold group while $B_3(Θ_m)$ is not even quasi-isometric to a $3$-manifold group for $m \geq 7$. |
| title | Manifold models for hyperbolic graph braid groups on three strands |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2603.07807 |