Matrix Representation of Knot and Link Groups
J. Peter May · Scholarship @ Claremont (The Claremont Colleges) · 2006
In the 1960s French mathematician George de Rham found a relationship between two invariants of knots. He found that there exist representations of the fundamental group of a knot into a group G of upper right triangular matrices in C with determinant one that is described exactly by the roots of the Alexander polynomial. I extended this result to find that the representations of the fundamental group of a link into G are described by the multivariable Alexander polynomial of the link.