A self-linking invariant of virtual knots
A self-linking invariant of virtual knots
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DOI：
10.4064/fm184-0-10
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发表时间：
2004-05
影响因子：
0.6
通讯作者：
L. Kauffman
中科院分区：
文献类型：
--
作者：
L. Kauffman
本文引入了虚结点和虚链路的一个新的不变量，它对许多虚结点和虚链路是非平凡的，但在经典结点和虚链路上是平凡的。不变量最初将表示为括号多项式[4]的相关项，然后从该多项式中提取其指数项，特别是对于结的情况。括号多项式的类比将表示为{K}（用花括号），并称为二元括号多项式。关于二进制括号的定义和属性，请参见第3节。这个不变量的组合的关键是用相关图的2色来解释状态和。
In this paper we introduce a new invariant of virtual knots and links that is non-trivial for many virtuals, but is trivial on classical knots and links. The invariant will initially be expressed in terms of a relative of the bracket polynomial [4], and then extracted from this polynomial in terms of its exponents, particularly for the case of knots. The analog of the bracket polynomial will be denoted {K} (with curly brackets) and called the binary bracket polynomial. See Section 3 for the definition and properties of the binary bracket. The key to the combinatorics of this invariant is an interpretation of the state sum in terms of 2-colorings of the associated diagrams.