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arxiv: math/0006112 · v1 · pith:LV6VPHAFnew · submitted 2000-06-15 · 🧮 math.GT

Knots and Contact Geometry

John B. Etnyre , Ko Honda This is my paper
classification 🧮 math.GT
keywords knotscontacteightfigureisotopylegendriantorustransversal
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We classify Legendrian torus knots and figure eight knots in the tight contact structure on the 3-sphere up to Legendrian isotopy. As a corollary to this we also obtain the classification of transversal torus knots and figure eight knots up to transversal isotopy.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A New CR Invariant for Contact 3-Manifolds and Classes of Open Books

    math.GT 2026-06 unverdicted novelty 7.0

    Defines a new CR invariant μ_M(ξ) ∈ Pic_C(M) for contact 3-manifolds that is independent of supporting open book via Giroux correspondence and distinguishes two tight structures on T^3 via differing first Chern classes.

  2. A New CR Invariant for Contact 3-Manifolds and Classes of Open Books

    math.GT 2026-06 unverdicted novelty 6.0

    Defines μ_M(ξ) in Pic_C(M) for contact 3-manifolds via open book embeddings into C^3 and Stein theory, independent by Giroux correspondence, and distinguishes tight structures on T^3 via first Chern classes.