Legendrian and Transverse Twist Knots
نویسندگان
چکیده
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m(52) 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−2n with crossing number 2n+1. In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that K−2n has exactly ⌈ 2 2 ⌉ Legendrian representatives with maximal Thurston–Bennequin number, and ⌈ 2 ⌉ transverse representatives with maximal self-linking number. Our techniques include convex surface theory, Legendrian ruling invariants, and Heegaard Floer homology.
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