Knot Polynomials: Myths and Reality
Slavik Jablan, Ljiljana Radovic
TL;DR
This paper reviews and compares various polynomial invariants of knots and links, analyzing their relative strengths and limitations in knot theory.
Contribution
It offers a comprehensive overview of the key polynomial invariants used in knot theory, clarifying misconceptions and highlighting their practical differences.
Findings
Alexander polynomial's limitations in distinguishing knots
Jones polynomial's effectiveness in knot classification
Khovanov polynomial's categorification advantages
Abstract
This article provides an overview of relative strengths of polynomial invariants of knots and links, such as the Alexander, Jones, Homflypt, Kaufman two-variable polynomial, and Khovanov polynomial.
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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematics and Applications · Advanced Numerical Analysis Techniques