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Application of Braiding Sequences. II. Polynomial Invariants of Positive Knots

Part of: Combinatorics Arithmetic rings and other special rings Low-dimensional topology

Published online by Cambridge University Press:  03 March 2016

A. Stoimenow
A. Stoimenow*
Affiliation:
School of General Studies, Gwangju Institute of Science and Technology, GIST College, 123 Cheomdan-gwagiro, Gwangju 500-712, Republic of Korea (stoimeno@stoimenov.net)
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Abstract

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We apply the concept of braiding sequences to link polynomials to show polynomial growth bounds on the derivatives of the Jones polynomial evaluated on S1 and of the Brandt–Lickorish–Millett–Ho polynomial evaluated on [–2, 2] on alternating and positive knots of given genus. For positive links, boundedness criteria for the coefficients of the Jones, HOMFLY and Kauffman polynomials are derived. (This is a continuation of the paper ‘Applications of braiding sequences. I’: Commun. Contemp. Math.12(5) (2010), 681–726.)

Keywords

alternating knotpositive knotbraid indexgenuslink polynomialCasson–Walker invariant

MSC classification

Secondary: 57M25: Knots and links in $S^3$ 57M27: Invariants of knots and 3-manifolds 13F20: Polynomial rings and ideals; rings of integer-valued polynomials 05A15: Exact enumeration problems, generating functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 4 , November 2016 , pp. 1037 - 1064
Copyright
Copyright © Edinburgh Mathematical Society 2016