Open AccessMathematics

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

John B. Etnyre, K. Honda

2001.12.1Journal of Symplectic Geometry

DOI: 10.4310/jsg.2001.v1.n1.a3

tlooto Summary

Classifying Legendrian torus knots and figure eight knots in tight contact structures up to Legendrian isotopy.

Abstract

We classify Legendrian torus knots and Legendrian gure eight knots in the tight contact structure on S up to Legendrian isotopy. As a corollary to this we also obtain the classi cation of transversal torus knots and transversal gure eight knots up to transversal isotopy.

Citation format

ETNYRE, John B.; HONDA, K. Knots and contact geometry i: Torus knots and the figure eight knot. Journal of Symplectic Geometry, 2001, 1: 63–120.