Mutation and the colored Jones polynomial

2006/07/31 by A. Stoimenow, T. Tanaka, Stoimenow, Alexander +1
Computer Science · Mathematics · #57M25 #57N70 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #semigroups and automata theory

paper · doi:10.48550/arxiv.math/0607794

openalex publication_date 2006/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show examples of knots with the same polynomial invariants and hyperbolic volumes, with variously coinciding 2-cable polynomials and colored Jones polynomials, which are not mutants.

Citations

• The universal Vassiliev-Kontsevich invariant for framed oriented links
• Does the Jones polynomial determine the signature of a knot?

Related

• Knot polynomials and generalized mutation
• On the head and the tail of the colored Jones polynomial
• Knot Cabling and the Degree of the Colored Jones Polynomial II
• Colored HOMFLY polynomials that distinguish mutant knots
• Colored Jones Polynomials and the Volume Conjecture