2012/11/07 by Lena C. Folwaczny, Louis H. Kauffman, Folwaczny, Lena C. +1
Computer Science · Mathematics · #Algorithms and Data Compression #Artificial Intelligence in Games #Geometric and Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.1211.1747
27 pages, 34 figures
arxiv created 2012/11/08 · arxiv updated 2012/11/09
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.