Differential 3-knots in 5-space with and without self-intersections
Differential 3-knots in 5-space with and without self-intersections
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5 空间中带或不带自相交的差动 3 结
DOI：
10.1016/s0040-9383(99)00058-0
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Ekholm
中科院分区：
文献类型：
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作者：
T. Ekholm
浸入S3→ R5的正则同伦类构成无限循环群。包含嵌入的类形成索引为24的子群。一般的浸入是定期同伦的嵌入的障碍被描述在其自交的几何不变量。利用自相交的几何性质构造了类属浸入的两个不变量J和St，它们类似于平面曲线的Arnold不变量。我们证明了J和St是独立的一阶不变量，并且任何一阶不变量都是它们的线性组合。作为副产品，得到了浸入S3→ R4的一些不变量。使用它们，我们发现限制的拓扑结构的自相交。
Regular homotopy classes of immersions S3→ R5constitute an infinite cyclic group. The classes containing embeddings form a subgroup of index 24. The obstruction for a generic immersion to be regularly homotopic to an embedding is described in terms of geometric invariants of its self-intersection. Geometric properties of self-intersections are used to construct two invariants J and St of generic immersions which are analogous to Arnold's invariants of plane curves . We prove that J and St are independent first-order invariants and that any first-order invariant is a linear combination of these. As by-products, some invariants of immersions S3→ R4are obtained. Using them, we find restrictions on the topology of self-intersections.