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Legendrian and transverse twist knots

John B. EtnyreLenhard L. NgVera Vértesi — 2013

Journal of the European Mathematical Society

In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m ( 5 2 ) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot K - 2 n with crossing number 2 n + 1 . In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that K - 2 n has exactly n 2 2 Legendrian representatives with maximal Thurston–Bennequin...

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