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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.07610 |
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Table of 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 $π_1(S^3 \setminus R)^{(2)}.$