Knot Polynomials: Myths and Reality
Slavik Jablan, Ljiljana Radovic
TL;DR
This paper reviews various polynomial invariants of knots and links, comparing their strengths and limitations in distinguishing knots, detecting primeness, and their algebraic properties.
Contribution
It offers a comprehensive overview of the relative strengths and limitations of key polynomial invariants and homology theories in knot theory.
Findings
Alexander polynomial's limitations in knot distinction
Jones polynomial's effectiveness in knot detection
Khovanov homology'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, and Kaufman two-variable polynomial, Khovanov homology, factorizability of the polynomials, and knot primeness detection.
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Taxonomy
TopicsGeometric and Algebraic Topology · Orthopedic Surgery and Rehabilitation