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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13326 |
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| _version_ | 1866911804659073024 |
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| author | Armas-Sanabria, Lorena Eudave-Muñoz, Mario Díaz-González, Juan Pablo Hinojosa-Palafox, Gabriela |
| author_facet | Armas-Sanabria, Lorena Eudave-Muñoz, Mario Díaz-González, Juan Pablo Hinojosa-Palafox, Gabriela |
| contents | An integral framed, closed pure n-braid B' in the 3-sphere describes a positive Artin presentation, if the braid B can be put on a disk with holes such that each relation describes a positive path and these paths are disjoint. In the present paper we classify the closed, pure n-braids B' in the 3-sphere, such that B represents a positive Artin presentation. Also we prove that if such B describes a positive Artin presentation then B' is strongly invertible. Such positive Artin presentation give us the fundamental group of closed, connected and orientable 3-manifolds M, and in fact, by giving an example, we show that there exist 3-manifolds whose fundamental group does not admit a positive Artin presentation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive Artin Presentations Armas-Sanabria, Lorena Eudave-Muñoz, Mario Díaz-González, Juan Pablo Hinojosa-Palafox, Gabriela Geometric Topology 57M05, 57K10 An integral framed, closed pure n-braid B' in the 3-sphere describes a positive Artin presentation, if the braid B can be put on a disk with holes such that each relation describes a positive path and these paths are disjoint. In the present paper we classify the closed, pure n-braids B' in the 3-sphere, such that B represents a positive Artin presentation. Also we prove that if such B describes a positive Artin presentation then B' is strongly invertible. Such positive Artin presentation give us the fundamental group of closed, connected and orientable 3-manifolds M, and in fact, by giving an example, we show that there exist 3-manifolds whose fundamental group does not admit a positive Artin presentation. |
| title | Positive Artin Presentations |
| topic | Geometric Topology 57M05, 57K10 |
| url | https://arxiv.org/abs/2403.13326 |