THE Ck-GORDIAN COMPLEX OF KNOTS
THE Ck-GORDIAN COMPLEX OF KNOTS
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DOI：
10.1142/s0218216506004300
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发表时间：
2006
影响因子：
0.5
通讯作者：
Y. Ohyama
中科院分区：
文献类型：
--
作者：
Y. Ohyama
Hirasawa和Uchida定义了纽结的Gordian复形，这是一种简单的复形，它的顶点由S3中的所有纽结类型组成，他们使用“交叉变换”。本文定义了纽结的k-Gordian复形，它是纽结的Gordian复形的推广。设k是大于2的自然数，我们证明了对于任意的结点K0和任意给定的自然数n，都存在一个结点族{K0，K1，…，Kn}使得对于族的任何一对不同元素(ki，Kj)，Ck-距离dCK(ki，Kj)=1。
Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S3 by using "a crossing change". In this paper, we define the Ck-Gordian complex of knots which is an extension of the Gordian complex of knots. Let k be a natural number more than 2 and we show that for any knot K0 and any given natural number n, there exists a family of knots {K0, K1,…, Kn} such that for any pair (Ki, Kj) of distinct elements of the family, the Ck-distance dCk(Ki, Kj) = 1.