We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Coefficients and non-triviality of the Jones polynomial.
- Authors
Stoimenow, Alexander
- 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.
- Subjects
POLYNOMIALS; CHARTS, diagrams, etc.; HYPERBOLIC differential equations; GRAPHIC methods; ALGEBRA
- Publication
Journal für die Reine und Angewandte Mathematik, 2011, Vol 2011, Issue 657, p1
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/CRELLE.2011.047