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.
Knots and Contact Geometry
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abstract
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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math.GT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A New CR Invariant for Contact 3-Manifolds and Classes of Open Books
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.