STRUCTURED GROUPS AND LINK-HOMOTOPY
STRUCTURED GROUPS AND LINK-HOMOTOPY
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结构化群和链接同伦
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发表时间：
1993
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通讯作者：
J. R. Hughes
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作者：
J. R. Hughes
我们使用具有从子午经度对派生的外围结构的简化群来研究三个球体中的链接同伦类。考虑了两种类型的外围结构——米尔诺的原始版本（在莱文的术语中称为“前外围结构”）和莱文的改进版（简称为“外围结构”）。我们在这里表明，前外围结构不足以将链接分类为链接同伦，并且 Levine 的外围结构虽然足够强大以区分那些未由前外围结构区分的类别，但也很可能不足以区分所有链接同伦类别。遵循 Levine 的分类程序，我们使用 Habegger 和 Lin 的工作建议的阻塞理论方法来比较结构保持和可实现的自同构。我们发现这些自同构群通常是不同的，因此需要更复杂的程序来按结构化群进行分类。
We study link-homotopy classes of links in the three sphere using reduced groups endowed with peripheral structures derived from meridian-longitude pairs. Two types of peripheral structures are considered — Milnor’s original version (called “pre-peripheral structures” in Levine’s terminology) and Levine’s refinement (called simply “peripheral structures”). We show here that pre-peripheral structures are not strong enough to classify links up to link-homotopy, and that Levine’s peripheral structures, although strong enough to distinguish those classes not distinguished by pre-peripheral structures, are also in all likelihood not strong enough to distinguish all link-homotopy classes. Following Levine’s classification program, we compare structure-preserving and realizable automorphisms, using an obstruction-theoretic approach suggested by work of Habegger and Lin. We find that these automorphism groups are in general different, so that a more complex program for classification by structured groups is required.