Homology cobordisms of 3-manifolds, knot concordances, and prime knots
Homology cobordisms of 3-manifolds, knot concordances, and prime knots
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3-流形的同调配边、结协调和素结
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发表时间：
1981
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通讯作者：
C. Livingston
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作者：
C. Livingston
Kirby和Lickorish [3]以前使用不同的构造获得了第二个结果。这回答了Gordon [2]中的第13个问题。Schubert [6]的结果证明了所构造的纽结是素的。在本文的后半部分，我们将推广他的结果来刻画素“广义”索结。如果JSΓX是S x B中的纽结，并且K2是S中的纽结，则我们可以通过将S x B映射到S来形成K2的Kx电缆，其中S x {0}去往K2。我们将证明，在一个明显的限制下，K2的Kt索是素的当且仅当Kx在S1 x B中是素的.最后一节给出了一大组素结在S x B中的例子。我要感谢Rob Kirby的有益建议和对话。
Kirby and Lickorish [3] have previously obtained the second result using a different construction. This answers problem 13 in Gordon [2]. Results of Schubert [6] show that the knots constructed are prime. In the second half of this paper we will generalize his results to characterize prime "generalized" cable knots. If JSΓX is a knot in S x B and K2 is a knot in S , we can form the Kx cable of K2 by mapping S x B into S, with S x {0} going to K2. We will show that, with an obvious restriction, the Kt cable of K2 is prime if and only if Kx is prime in S 1 x B. The final section gives a large set of examples of prime knots in S x B. I would like to thank Rob Kirby for his helpful suggestions and conversations.