Legendrian knots and links classified by classical invariants

Details Legendrian knots and links classified by classical invariants Legendrian knots and links classified by classical invariants

2005-03-02

arxiv.org/abs/math/0503033v1

Commun. Contemp. Math. 9 (2007), 135-162

Mathematics

Symplectic Geometry

22 pages

Scientific paper

It is shown that Legendrian (resp. transverse) cable links in the 3-sphere with its standard tight contact structure, i.e. links consisting of an unknot and a cable of that unknot, are classified by their oriented link type and the classical invariants (Thurston-Bennequin invariant and rotation number in the Legendrian case, self-linking number in the transverse case). The analogous result is proved for torus knots in the 1-jet space of the circle with its standard tight contact structure.

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