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<p>Ozsváth 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.</p>

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Legendrian non-simple Whitehead doubles of the trefoil

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Saliha Kivanç

摘要

Ozsváth 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.