The world according to the Fox Matrix
by
Oliver Dasbach
Louisiana State University

Fox gave a way to compute the Alexander polynomial of a knot via a matrix of

Fox derivatives of knot group relations. Later on this matrix proved to be useful in

the definition of the twisted Alexander polynomial, the computation of the

volume of hyperbolic knots and - via Kauffman's state model for the Alexander

polynomial - in the computation of Ozsvath and Szabo's Heegard Floer

Homology for knots.

We will reflect on these different aspects.

Date received: February 24, 2005