Band description of knots and Vassiliev invariants
Band description of knots and Vassiliev invariants
复制标题
结和 Vassiliev 不变量的带描述
DOI：
10.1017/s0305004102006138
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发表时间：
2000
影响因子：
0.8
通讯作者：
A. Yasuhara
中科院分区：
文献类型：
--
作者：
Kouki Taniyama;A. Yasuhara
在20世纪90年代，Habiro定义了每个自然数k的有向链的Ck-移动[5]。一个Ck-移动是一种定向链接的局部移动，两个定向节点具有相同的k-1阶瓦西里耶夫不变量当且仅当它们通过Ck-移动相互转化。因此，他成功地推导出一个几何结论，从代数条件。然而，这个定理只出现在他最近的论文[6]中，他在论文中发展了他最初的clasper理论，并作为clasper理论的结果得到了这个定理。我们注意到，定理的“如果”部分也在[4]，[9]，[10]和[16]中给出，在[13]中，斯坦福大学给出了具有相同的Vassiliev k−1阶不变量的结的另一个特征。
In the 1990s, Habiro defined Ck-move of oriented links for each natural number k [5]. A Ck-move is a kind of local move of oriented links, and two oriented knots have the same Vassiliev invariants of order [les ] k−1 if and only if they are transformed into each other by Ck-moves. Thus he has succeeded in deducing a geometric conclusion from an algebraic condition. However, this theorem appears only in his recent paper [6], in which he develops his original clasper theory and obtains the theorem as a consequence of clasper theory. We note that the ‘if’ part of the theorem is also shown in [4], [9], [10] and [16], and in [13] Stanford gives another characterization of knots with the same Vassiliev invariants of order [les ] k−1.