Writhe polynomials and shell moves for virtual knots and links
Writhe polynomials and shell moves for virtual knots and links
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DOI：
10.1016/j.ejc.2019.103033
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Takuji Nakamura;Yasutaka Nakanishi;S. Satoh
中科院分区：
文献类型：
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作者：
Takuji Nakamura;Yasutaka Nakanishi;S. Satoh
扭多项式是有向虚纽结的基本不变量。我们引入了一套本地移动定向虚拟节点称为壳移动。本文的第一个目的是证明两个有向虚纽结具有相同的扭振多项式当且仅当它们由一个有限的壳运动序列相关。本文的第二个目的是分类定向2分量虚拟链接壳移动通过使用虚拟链接的几个不变量。
The writhe polynomial is a fundamental invariant of an oriented virtual knot. We introduce a set of local moves for oriented virtual knots called shell moves. The first aim of this paper is to prove that two oriented virtual knots have the same writhe polynomial if and only if they are related by a finite sequence of shell moves. The second aim of this paper is to classify oriented 2-component virtual links up to shell moves by using several invariants of virtual links.