Legendrian Non-simple Whitehead Doubles Of The Trefoil
Abstract
Ozsv\'ath and Stipsicz showed that some Eliashberg-Chekanov twist knots, which are Whitehead doubles of the unknot, are not Legendrian simple. We extend their result by considering some Whitehead doubles of the trefoil: Using properties of knot Floer homology and the distinguished surgery triangle, we show that this family of knots is Legendrian non-simple in the standard contact 3-sphere.
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