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Maximal Thurston–Bennequin number of two-bridge links

Lenhard Ng

Algebraic & Geometric Topology 1 (2001) 427–434

arXiv: math.GT/0008242

Abstract

We compute the maximal Thurston–Bennequin number for a Legendrian two-bridge knot or oriented two-bridge link in standard contact 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
Mathematical Subject Classification 2000
Primary: 53D12
Secondary: 57M15
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Publication
Received: 24 May 2001
Revised: 26 July 2001
Accepted: 27 July 2001
Published: 31 July 2001
Authors
Lenhard Ng
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge MA 02139
USA
http://www-math.mit.edu/~lenny/