A criterion for double sliceness
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913433418465280 |
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| author | Conway, Anthony |
| author_facet | Conway, Anthony |
| contents | We describe a condition involving noncommutative Alexander modules which ensures that a knot with Alexander module $\mathbb{Z}[t^{\pm 1}]/(t-2) \oplus \mathbb{Z}[t^{\pm 1}]/(t^{-1}- 2)$ is topologically doubly slice. As an application, we show that a satellite knot $R_η(K)$ is doubly slice if the pattern $R$ has Alexander module $\mathbb{Z}[t^{\pm 1}]/(t- 2) \oplus \mathbb{Z}[t^{\pm 1}]/(t^{-1}- 2)$ and satisfies this condition, and if the infection curve $η\subset S^3 \setminus R$ lies in the second derived subgroup $π_1(S^3 \setminus R)^{(2)}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07610 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A criterion for double sliceness Conway, Anthony Geometric Topology We describe a condition involving noncommutative Alexander modules which ensures that a knot with Alexander module $\mathbb{Z}[t^{\pm 1}]/(t-2) \oplus \mathbb{Z}[t^{\pm 1}]/(t^{-1}- 2)$ is topologically doubly slice. As an application, we show that a satellite knot $R_η(K)$ is doubly slice if the pattern $R$ has Alexander module $\mathbb{Z}[t^{\pm 1}]/(t- 2) \oplus \mathbb{Z}[t^{\pm 1}]/(t^{-1}- 2)$ and satisfies this condition, and if the infection curve $η\subset S^3 \setminus R$ lies in the second derived subgroup $π_1(S^3 \setminus R)^{(2)}.$ |
| title | A criterion for double sliceness |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2310.07610 |