Hypercube diagrams for knots, links, and knotted tori

For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. Finally, there is a generalization of cube diagrams, called hypercube diagrams. We use such diagrams, which represent immersed Lagrangian tori in R^4 to study embedded Legendrian tori in the standard contact space. We then show how to compute one of the classical invariants, the rotation class, and discuss applications to contact homology.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2012

Author dc:creator

• McCarty, Ben

• knots
• links
• contact
• Legendrian

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-05252012-130050
https://repository.lsu.edu/gradschool_dissertations/552

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1551