On Fox's congruence classes of knots. II
On Fox's congruence classes of knots. II
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关于福克斯结的同余类。
DOI：
10.18910/6597
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发表时间：
1990
影响因子：
0.4
通讯作者：
Yasutaka Nakanishi
中科院分区：
文献类型：
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作者：
Yasutaka Nakanishi
R.H.Fox在文[3]中引入了纽结同余类的概念，并用Alexander矩阵和多项式给出了同余的一个必要条件。S.Suzuki和作者[9]改进了他的条件，证明了当nφL和(n，#)Φ(2，1)，(2，2)时，存在无穷多个模n，q的纽结同余类。进一步，他们猜想所有的纽结都是模2，1和2，2的同余。在这篇注记中，我们将推广环的同余类的概念，并给出一个替代条件。证明了两个环是模2，1同余的当且仅当这两个环是Z2link同调的。(模2，1的^.-分支环的同余类数正好是2~“。)作为推论，我们得到所有的纽结都是模2，1的同余。
R.H. Fox introduced the notion of congruence class of knots in [3], and he gave a necessary condition for congruence in terms of Alexander matrices and polynomials. S. Suzuki and the author [9] improved his condition and showed that there exist infinitely many congruence classes of knots modulo n, q if nφl and (n, #)Φ(2, 1), (2, 2). Further, they conjectured that all knots are congruent modulo 2, 1 and 2, 2. In this note we will generalize the notion of congruence class for links and give an alternate condition. And we will prove that two links are congruent modulo 2, 1 if and only if the two links are Z2link-homologous. (The number of congruence classes of ^.-component links modulo 2, 1 is just 2~".) As a corollary, we have that all knots are congruent modulo 2, 1.