A cabling formula for the colored Jones polynomial

Abstract

We prove an explicit cabling formula for the colored Jones polynomial. As an application we prove the volume conjecture for all zero volume knots and links, i.e. all knots and links that are obtained from the unknot by repeated cabling and connected sum.

12 pages, 3 figures

References in corpus (3)

• On the characteristic and deformation varieties of a knot
• Quantum Knot Invariant for Torus Link and Modular Forms
• An introduction to the volume conjecture and its generalizations

Cited by in corpus (7)

• The AJ-conjecture and cabled knots over the figure eight knot
• The slope conjecture for graph knots
• Iterated torus knots and double affine Hecke algebras
• Knot Cabling and the Degree of the Colored Jones Polynomial
• The strong slope conjecture for cablings and connected sums
• A slope conjecture for links
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot