A Linking Number Definition of the Affine Index Polynomial and Applications
A Linking Number Definition of the Affine Index Polynomial and Applications
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DOI：
10.1142/s0218216513410046
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发表时间：
2012-11
期刊：
影响因子：
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通讯作者：
Lena C. Folwaczny;L. Kauffman
中科院分区：
文献类型：
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作者：
Lena C. Folwaczny;L. Kauffman
利用虚链接数给出了仿射指数多项式(称为扭动多项式)的另一种定义，并探讨了这种多项式的应用。特别地，证明了奇虚结和纯虚结的化妆交叉变换猜想。它还证明了该多项式可以通过正向旋转检测突变，并证明了它不能通过正向反射检测突变。最后，它展示了一对突变的纽结，可以通过来自多项式的类型2瓦西里耶夫不变量来区分。
This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial. In particular, it proves the Cosmetic Crossing Change Conjecture for odd virtual knots and pure virtual knots. It also demonstrates that the polynomial can detect mutations by positive rotation and proves it cannot detect mutations by positive reflection. Finally it exhibits a pair of mutant knots that can be distinguished by a Type 2 Vassiliev Invariant coming from the polynomial.