A computer evaluation of topological knots

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.