Title page for ETD etd-05252012-130050

Type of Document

Dissertation

Author

McCarty, Ben

URN

etd-05252012-130050

Title

Hypercube diagrams for knots, links, and knotted tori

Degree

Doctor of Philosophy (Ph.D.)

Department

Mathematics

Advisory Committee

Advisor Name	Title
Baldridge, Scott	Committee Chair
Dasbach, Oliver	Committee Member
Davidson, Mark	Committee Member
Delzell, Charles	Committee Member
Gilmer, Pat	Committee Member
Van Scotter, James R	Dean's Representative

Keywords

knots
links
contact
Legendrian

Date of Defense

2012-05-01

Availability

unrestricted

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.

Files

Filename		Size	Approximate Download Time (Hours:Minutes:Seconds)
Filename		Size	28.8 Modem	56K Modem	ISDN (64 Kb)	ISDN (128 Kb)	Higher-speed Access
	CatalogingAbstract.pdf	4.73 Kb	00:00:01	< 00:00:01	< 00:00:01	< 00:00:01	< 00:00:01
	DissertationMcCarty.pdf	4.77 Mb	00:22:05	00:11:21	00:09:56	00:04:58	00:00:25