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

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

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

We apply the concept of braiding sequences to link polynomials to show polynomial growth bounds on the derivatives of the Jones polynomial evaluated on S 1 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

Information

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 

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