Maximal Thurston-Bennequin number of two-bridge links
type: Item
instance of: scholarly article
title: Maximal Thurston-Bennequin number of two-bridge links
zbMATH Open document ID: 1056.57010
author: Lenhard Ng
published in: Algebraic \& Geometric Topology
publication date: 2001-07-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0008242
full work available at URL: https://eudml.org/doc/124246
full work available at URL: agt-1-21.abs.html
review text: The author determines the maximal Thurston-Bennequin number for a two-bridge knot or oriented two-bridge link in the standard contact structure, by showing that the upper bound in terms of the Kauffman polynomial due to \textit{L. Rudolf} [Math. Proc. Camb. Philos. Soc. 107, No. 2, 319--327 (1990; Zbl 0703.57005)] and \textit{S. Tabachnikov} [Math. Res. Lett. 4, No. 1, 143--156 (1997; Zbl 0877.57001)] is sharp. As an application, he determines the maximal Thurston-Bennequin number for prime knots with \(\leq 9\) crossings, except the mirror image of the \(9_{42}\) knot in Rolfsen's table.
reviewed by: Makoto Sakuma
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57R17
zbMATH DE Number: 1627575
zbMATH Keywords: Legendrian knot
zbMATH Keywords: two-bridge knot
zbMATH Keywords: Thurston-Bennequin number
zbMATH Keywords: Kauffman polynomial
MaRDI profile type: Publication
OpenAlex ID: W2150163848
arXiv ID: math/0008242
cites work: Q3692516
cites work: Knots
cites work: Knots and contact geometry. I: Torus knots and the figure eight knot.
cites work: On Legendrian knots and polynomial invariants
cites work: Invariants of Legendrian and transverse knots in the standard contact space
cites work: On Knots. (AM-115)
cites work: Linear skein theory and link polynomials
cites work: Q4886696
cites work: Q4877336
cites work: A congruence between link polynomials
cites work: Knoten mit zwei Brücken
cites work: Estimates for the Bennequin number of Legendrian links from state models for knot polynomials
cites work: Maximal Bennequin numbers and Kauffman polynomials of positive links
DOI: 10.2140/AGT.2001.1.427
description: scientific article; zbMATH DE number 1627575