#### Volume 1, issue 1 (2001)

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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 ${ℝ}^{3}$, 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
Primary: 53D12
Secondary: 57M15