Intermediate subgroups of braid groups are not bi-orderable
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915585073348608 |
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| author | Cruz, R. M. de A. |
| author_facet | Cruz, R. M. de A. |
| contents | Let $M$ be the disk or a compact, connected surface without boundary different from the sphere $S^2$ and the real projective plane $\mathbb{R}P^2$, and let $N$ be a compact, connected surface (possibly with boundary). It is known that the pure braid groups $P_n(M)$ of $M$ are bi-orderable, and, for $n\geq 3$, that the full braid groups $B_n(M)$ of $M$ are not bi-orderable. The main purpose of this article is to show that for all $n \geq 3$, any subgroup $H$ of $B_n(N)$ that satisfies $P_n(N) \subsetneq H \subset B_n(N)$ is not bi-orderable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intermediate subgroups of braid groups are not bi-orderable Cruz, R. M. de A. Geometric Topology Algebraic Topology 20F36, 20F60, 06F15 Let $M$ be the disk or a compact, connected surface without boundary different from the sphere $S^2$ and the real projective plane $\mathbb{R}P^2$, and let $N$ be a compact, connected surface (possibly with boundary). It is known that the pure braid groups $P_n(M)$ of $M$ are bi-orderable, and, for $n\geq 3$, that the full braid groups $B_n(M)$ of $M$ are not bi-orderable. The main purpose of this article is to show that for all $n \geq 3$, any subgroup $H$ of $B_n(N)$ that satisfies $P_n(N) \subsetneq H \subset B_n(N)$ is not bi-orderable. |
| title | Intermediate subgroups of braid groups are not bi-orderable |
| topic | Geometric Topology Algebraic Topology 20F36, 20F60, 06F15 |
| url | https://arxiv.org/abs/2510.24947 |