Fibered knots with the same $0$-surgery and the slice-ribbon conjecture
Fibered knots with the same $0$-surgery and the slice-ribbon conjecture
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DOI：
10.4310/mrl.2016.v23.n2.a1
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
Tetsuya Abe;Keiji Tagami
中科院分区：
文献类型：
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作者：
Tetsuya Abe;Keiji Tagami
Akbulut 和 Kirby 推测具有相同 $0$ 手术的两个结是一致的。在本文中，我们证明如果切片带猜想为真，则修改后的 Akbulut-Kirby 猜想为假。我们还给出了切片带猜想的纤维潜在反例。
Akbulut and Kirby conjectured that two knots with the same $0$-surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.