Zeros of Jones Polynomials for Families of Knots and Links

Abstract

We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial. For each of these families we determine the zeros of the Jones polynomial, including the accumulation set in the limit of infinitely many crossings. A discussion is also given of the calculation of Jones polynomials for non-alternating links.

30 pages, latex, 9 postscript figures; minor rewording on a reference, no changes in results

References in corpus (2)

• Zeroes of the Jones polynomial
• Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice

Cited by in corpus (11)

• A Little Statistical Mechanics for the Graph Theorist
• Reliability Polynomials and their Asymptotic Limits for Families of Graphs
• On the Mahler measure of Jones polynomials under twisting
• Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips
• Transfer Matrices for the Partition Function of the Potts Model on Cyclic and Mobius Lattice Strips
• Exact Results for Average Cluster Numbers in Bond Percolation on Lattice Strips
• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips
• Evaluating the Jones polynomial with tensor networks
• Three-partite vertex model and knot invariants
• Partition Function Zeros of a Restricted Potts Model on Self-Dual Strips of the Square Lattice
• Jones Polynomials and their Zeros for a Family of Knots and Links