Knots and Contact Geometry

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.

References in corpus (2)

• On the classification of tight contact structures I
• On the non-existence of tight contact structures

Cited by in corpus (17)

• Contact homology and one parameter families of Legendrian knots
• Maximal Thurston-Bennequin Number of Two-Bridge Links
• On arc index and maximal Thurston-Bennequin number
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• Duality for Legendrian contact homology
• Augmentations and Rulings of Legendrian Knots
• Studying uniform thickness I: Legendrian simple iterated torus knots
• Contact surgery and supporting open books
• Non-looseness of non-loose knots
• Legendrian Submanifolds in $R^{2n+1}$ and Contact Homology
• Legendrian Hopf links
• The Surgery Unknotting Number of Legendrian Links
• Non-loose negative torus knots
• Computable Legendrian invariants
• On the additivity of the Thurston--Bennequin invariant of Legendrian knots
• Invariants of Legendrian Knots and Coherent Orientations
• On Legendrian knots and polynomial invariants