Concordance implies homotopy for classical links inM3
Concordance implies homotopy for classical links inM3
复制标题
一致性意味着 M3 中经典链接的同伦
DOI：
10.1007/bf02566279
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发表时间：
1979
影响因子：
0.9
通讯作者：
D. Goldsmith
中科院分区：
文献类型：
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作者：
D. Goldsmith
在本文中，我证明了协调蕴涵同伦的经典链接在任何3-流形。一致性的概念首先由Fox和Milnor在[2]中针对3中的节点提出，后来由FOX在[1]的问题25中扩展到R 3中的链接。Milnor在[5]中定义并研究了3-流形M3中的链的同伦，证明完全是几何的，而且相当简单。事实上，在这一点上，我会引导读者注意图4，它表明了从一个特定的带状链接到R3中的平凡链接的同伦。这样读者就可以证明所有带状链环都是零同伦的（引理2.3）。本文的结果也是查尔斯·吉芬（Charles Giffen）通过不同的方法独立获得的。
In this paper I prove that concordance implies homotopy for classical links in any 3-manifold. The notion of concordance was first developed by Fox and Milnor in [2] for knots in a 3, and later extended to links in R 3 by FOX, in Problem 25 of [1]. Homotopy of links in a 3-manifold M 3 was defined and studied by Milnor in [5].The proof is entirely geometric, and also quite simple. In fact, at this point I would direct the reader's attention to Figure 4, which indicates a homotopy from a particular ribbon link to the trivial link in R 3. The reader might then be led to the proof that all ribbon links are null-homotopic (Lemma 2.3). The result of this paper has also been obtained by Charles Giffen, independently, and by a different method.