There exist inequivalent knots with the same complement
There exist inequivalent knots with the same complement
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存在具有相同补数的不等价结
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
J. Shaneson
中科院分区：
文献类型：
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作者：
S. Cappell;J. Shaneson
结的研究和分类是基于结补的不变量。本文给出了具有微分同构补的不等价光滑球节的例子。这些例子也不会是彼此的反射、反转或反射反转。我们所考虑的结可以被描述为具有一个刺穿的n-环面的所有纤维结的类，并且具有第一同调上的单调映射没有负特征值。通过简单的修改，参数表明构造的示例甚至不是分段线性或拓扑等效的。光滑n结是（n +2）球S ' +2的光滑子流形K，同胚于So，如果K同胚于S '，则说
The study and classification of knots has been based upon invariants of the knot complement. In this paper we give examples of inequivalent smooth spherical knots with diffeomorphic complements. These examples will also not be reflections, inversions or reflected inversions of each other. The knots we consider can be described as the class of all fibred knots with fibre a punctured n-torus, n > 3, and with the monodromy map on first homology having no negative eigenvalues. With easy modifications the arguments show that the constructed examples are not even piecewise linearly or topologically equivalent. A smooth n-knot is a smooth submanifold K of the (n + 2)-sphere S"+2, homeomorphic to So, and if K is diffeomorphic to S", it is said that the