Algebraic & Geometric Topology

Maximal Thurston–Bennequin number of two-bridge links

Lenhard Ng

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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.

Article information

Algebr. Geom. Topol., Volume 1, Number 1 (2001), 427-434.

Received: 24 May 2001
Revised: 26 July 2001
Accepted: 27 July 2001
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D12: Lagrangian submanifolds; Maslov index
Secondary: 57M15: Relations with graph theory [See also 05Cxx]

Legendrian knot two-bridge Thurston–Bennequin number Kauffman polynomial


Ng, Lenhard. Maximal Thurston–Bennequin number of two-bridge links. Algebr. Geom. Topol. 1 (2001), no. 1, 427--434. doi:10.2140/agt.2001.1.427.

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