REGULAR HOMOTOPY AND VASSILIEV INVARIANTS OF GENERIC IMMERSIONS Sk → ℝ2k-1, k ≥ 4
REGULAR HOMOTOPY AND VASSILIEV INVARIANTS OF GENERIC IMMERSIONS Sk → ℝ2k-1, k ≥ 4
复制标题
正则同伦和一般浸没的 VASSILIEV 不变量 Sk → ℝ2k-1, k ≥ 4
DOI：
10.1142/s0218216598000565
复制
发表时间：
1998
影响因子：
0.5
通讯作者：
T. Ekholm
中科院分区：
文献类型：
--
作者：
T. Ekholm
利用具有自然附加结构的自相交流形计算了一般浸入Sk → Sk 2k-1的正则同伦类。有一个自然的概念，瓦西里耶夫不变量的一般浸入。它们可以取任意阿贝尔群G中的值。证明了对任意m，m阶G-值模低阶不变量群同构于G，并且Vassiliev不变量不足以分离类属浸入，类属浸入不能通过正则同伦通过类属浸入相互得到.
The regular homotopy class of a generic immersion Sk → ℝ2k-1 is calculated in terms of its self intersection manifold with natural additional structures. There is a natural notion of Vassiliev invariants of generic immersions. These may take values in any Abelian group G. It is proved that, for any m, the group of mth order G-valued invariants modulo invariants of lower order is isomorphic to G and that the Vassiliev invariants are not sufficient to separate generic immersions, which can not be obtained from each other by a regular homotopy through generic immersions.