SIMPSON-DISSERTATION-2019.pdf (57.04 MB)
Download fileThe Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles
thesis
posted on 2019-08-06, 00:00 authored by David H. SimpsonWe 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 HChair
Kauffman, Louis HDepartment
Mathematics, Statistics and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral