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Coefficients and non-triviality of the Jones polynomial
Published/Copyright:
June 27, 2011
Abstract
Using an involved study of the Kauffman bracket, we give formulas for the second and third coefficient of the Jones polynomial in semiadequate diagrams. As applications, we show that several classes of links, including semiadequate links and Whitehead doubles of semiadequate knots, have non-trivial Jones polynomial. We also prove that there are infinitely many positive knots with no positive minimal crossing diagrams. Some relations to the twist number of a link, Mahler measure and the hyperbolic volume are given, for example explicit upper bounds on the volume for Montesinos and 3-braid links in terms of their Jones polynomial.
Received: 2008-09-22
Revised: 2009-11-06
Published Online: 2011-06-27
Published in Print: 2011-August
© Walter de Gruyter Berlin · New York 2011
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Articles in the same Issue
- Coefficients and non-triviality of the Jones polynomial
- Distribution of algebraic numbers
- Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs
- Characterizing quaternion rings over an arbitrary base
- Transcendence in positive characteristic and special values of hypergeometric functions
- Factoring 3-fold flips and divisorial contractions to curves
- Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
- -actions on UHF algebras of infinite type
