Algebraic and Geometric Topology 1 (2001), paper no. 21, pages 427-434.

Maximal Thurston-Bennequin Number of Two-Bridge Links

Lenhard L. Ng

Abstract. We compute the maximal Thurston-Bennequin number for a Legendrian two-bridge knot or oriented two-bridge link in standard contact R^3, by showing that the upper bound given by the Kauffman polynomial is sharp. As an application, we present a table of maximal Thurston-Bennequin numbers for prime knots with nine or fewer crossings.

Keywords. Legendrian knot, two-bridge, Thurston-Bennequin number, Kauffman polynomial

AMS subject classification. Primary: 53D12. Secondary: 57M15.

DOI: 10.2140/agt.2001.1.427

E-print: arXiv:math.GT/0008242

Submitted: 24 May 2001. (Revised: 26 July 2001.) Accepted: 27 July 2001. Published: 31 July 2001.

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Lenhard L. Ng
Department of Mathematics, Massachusetts Institute of Technology,
77 Massachusetts Avenue, Cambridge, MA 02139, USA
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