WebThe Alexander-Conway Polynomial. Alexander [K] [t] computes the Alexander polynomial of a knot K as a function of the variable t. Alexander [K, r] [t] computes a basis of the r'th Alexander ideal of K in Z [t]. The program Alexander [K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005. WebKeywords: Knots; Vassiliev invariants; Double dating tangle; Knot polynomials 1. Introduction In 1990, V.A. Vassiliev introduced the concept of a finite type invariant of knots, called Vassiliev invariants, by using singularity theory and algebraic topology [17]. These Vassiliev invariants provided us a unified framework in which to consider ...
arXiv:math/9304209v1 [math.GT] 1 Apr 1993
WebNov 4, 2002 · These two operations are unified to the hat-operation. For each Vassiliev invariant v of degree <=n, hat (v) is a Vassiliev invariant of degree <=n and the value hat … humangood cornerstone
Introduction to Vassiliev Knot Invariants - Semantic Scholar
WebWe prove that the construction of Vassiliev invariants by expanding the link polynomials P g,V (q, q −1) at the point q=1 is equivalent to the construction of Vassiliev invariants from … WebWe prove that the construction of Vassiliev invariants by expanding the link polynomials P g,V (q, q −1) at the point q=1 is equivalent to the construction of Vassiliev invariants from Chern-Simons perturbation theory.In both constructions a simple Lie algebra g and an irreducible representation V of g should be specified. Webinvariants are precisely as powerful as those polynomials. As invariants of finite type are much easier to define and manipulate than the quantum group invariants, it is likely that in attempting to classify knots, invariants of finite type will play a more fundamental role than the various knot polynomials. Contents 1. Introduction 2 1.1. humangood board of directors