SIMPSON-DISSERTATION-2019.pdf (57.04 MB)
Download file

The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles

Download (57.04 MB)
thesis
posted on 06.08.2019, 00:00 authored by David H. Simpson
We examine the relation between Ribbon Hopf Algebras and 1-1 Tangles -- knot diagrams that are cut at a point with the ends pulled apart. Specifically, we investigate the behavior of one such algebra, introduced in the 1992 paper "On Kauffman’s knot invariants arising from finite-dimensional Hopf algebras" by David Radford. We compile the first-ever results for knots of 3-10 crossings using one of these algebras, and discuss the magnitude of calculations involved, and practical methods of attaining results in reasonable time.

History

Advisor

Kauffman, Louis H

Chair

Kauffman, Louis H

Department

Mathematics, Statistics and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Radford, David Shalen, Peter Takloo-Bighash, Ramin Licht, Arthur

Submitted date

May 2019

Issue date

14/02/2019

Usage metrics

Categories

Exports