Identifier
etd-05252012-130050
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
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.
Date
2012
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
McCarty, Ben, "Hypercube diagrams for knots, links, and knotted tori" (2012). LSU Doctoral Dissertations. 552.
https://repository.lsu.edu/gradschool_dissertations/552
Committee Chair
Baldridge, Scott
DOI
10.31390/gradschool_dissertations.552