Isotopy and equivalence of knots in 3-manifolds
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866916029197713408 |
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| author | Aceto, Paolo Bregman, Corey Davis, Christopher W. Park, JungHwan Ray, Arunima |
| author_facet | Aceto, Paolo Bregman, Corey Davis, Christopher W. Park, JungHwan Ray, Arunima |
| contents | We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irreducible, closed, oriented $3$-manifolds we show the more general fact that every orientation preserving homeomorphism which preserves free homotopy classes of loops is isotopic to the identity. In the case of $S^1\times S^2$, we give infinitely many examples of knots whose isotopy classes are changed by the Gluck twist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_05796 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Isotopy and equivalence of knots in 3-manifolds Aceto, Paolo Bregman, Corey Davis, Christopher W. Park, JungHwan Ray, Arunima Geometric Topology 57K10, 57K30, 20F34, 20F65 We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irreducible, closed, oriented $3$-manifolds we show the more general fact that every orientation preserving homeomorphism which preserves free homotopy classes of loops is isotopic to the identity. In the case of $S^1\times S^2$, we give infinitely many examples of knots whose isotopy classes are changed by the Gluck twist. |
| title | Isotopy and equivalence of knots in 3-manifolds |
| topic | Geometric Topology 57K10, 57K30, 20F34, 20F65 |
| url | https://arxiv.org/abs/2007.05796 |