Knots and Contact Geometry I: Torus Knots and the Figure Eight Knot

We classify Legendrian torus knots and Legendrian figure eight knots in the tight contact structure on S³ up to Legendrian isotopy. A a corollary to this we also obtain the classification of transversal torus knots and transversal figure eight knots up to transversal isotopy.

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Published 1 January 2001