On the head and the tail of the colored Jones polynomial

2006/09/01 by Oliver T. Dasbach, Xiao-Song Lin · 89 citations
Mathematics · #Advanced Combinatorial Mathematics #Alternating polynomial #Bracket polynomial #Colored #Combinatorics #Corollary #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Jones polynomial #Knot theory #Mathematical analysis #Mathematics #Matrix polynomial #Physics #Polynomial

paper · pdf · doi:10.1112/s0010437x06002296

published in Compositio Mathematica 142(05), 1332-1342 (Cambridge University Press)

openalex publication_date 2006/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

The colored Jones polynomial is a function is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a volume-ish theorem for the colored Jones polynomial.

Cited by

• Higher Order Stability in the Coefficients of the Colored Jones Polynomial
• Quantum Invariants and Fiberedness
• Twist Regions and Coefficients Stability of the Colored Jones Polynomial
• The zero stability for the one-row colored \mathfraksl₃ Jones polynomial
• Sigma-Adequate Link Diagrams and the Tutte Polynomial
• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
• Twist formulas for one-row colored A₂ webs and \mathfraksl₃ tails of (2,2m)-torus links
• The tail of a quantum spin network
• Foundations of the Colored Jones Polynomial of singular knots
• On the quantum \mathfraksl₃ invariant of positive links
• Properties of closed 3-braids
• State Surfaces of Links
• Pretzel Knots and q-Series
• A stability conjecture for the colored Jones polynomial
• The Jones polynomial and graphs on surfaces
• Arborescent links and modular tails
• Gromov norm and Turaev-Viro invariants of 3-manifolds

Related

• Foundations of the Colored Jones Polynomial of singular knots
• The Head and Tail of the Colored Jones Polynomial for Adequate Knots
• The head and tail conjecture for alternating knots
• On the colored Jones polynomials of certain cable of the torus knots
• Stability properties of the colored Jones polynomial