Knots and Contact Geometry
John B. Etnyre, Ko Honda
TL;DR
This paper classifies Legendrian and transversal knots of specific types in the tight contact structure on the 3-sphere, providing a comprehensive understanding of their isotopy classes.
Contribution
It offers the first complete classification of Legendrian and transversal torus and figure eight knots in the tight contact structure on the 3-sphere.
Findings
Legendrian torus and figure eight knots classified up to isotopy
Transversal knots of these types also classified
Results enhance understanding of contact geometric knot theory
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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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Advanced Materials and Mechanics