Maximal Thurston–Bennequin number of two-bridge links

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

Mathematical Subject Classification 2000

Primary: 53D12

Secondary: 57M15

References

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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/

Volume 1, issue 1 (2001)

Lenhard Ng