Maximal Thurston-Bennequin number of two-bridge links. (English) Zbl 1056.57010

The author determines the maximal Thurston-Bennequin number for a two-bridge knot or oriented two-bridge link in the standard contact structure, by showing that the upper bound in terms of the Kauffman polynomial due to L. Rudolf [Math. Proc. Camb. Philos. Soc. 107, No. 2, 319–327 (1990; Zbl 0703.57005)] and S. Tabachnikov [Math. Res. Lett. 4, No. 1, 143–156 (1997; Zbl 0877.57001)] is sharp. As an application, he determines the maximal Thurston-Bennequin number for prime knots with \(\leq 9\) crossings, except the mirror image of the \(9_{42}\) knot in Rolfsen’s table.


57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M15 Relations of low-dimensional topology with graph theory
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57R17 Symplectic and contact topology in high or arbitrary dimension
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