A computer evaluation of topological knots

Author

Wallace G. Hynds

Date of Award

12-1982

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Robert J. Daverman

Committee Members

Kenneth Stephenson

Abstract

The purpose of this thesis is to present an algorithm to aid knot theorists in the classification of topological knots. To make the algorithm useful and available to knot theorists, it is specifically designed to be programmed on a microcomputer. A program in Z-80 assembler to execute the algorithm is presented.

Presentations of knot groups are rather easy to extract by hand from a given knot. Free derivatives are used to convert the presentation of the knot group to a Jacobian matrix. A reduction to one variable of the determinant of this matrix yields the Alexander polynomial. This Alexander polynomial is a powerful classification tool with the added feature of ease of comparison.

Recommended Citation

Hynds, Wallace G., "A computer evaluation of topological knots. " Master's Thesis, University of Tennessee, 1982.
https://trace.tennessee.edu/utk_gradthes/15026