Jess May

Harvey Mudd College Mathematics 2005

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Thesis Advisor: Prof. Jim Hoste
Second Reader: Prof. Francis Su
E-Mail: jmay@hmc.edu
Thesis Proposal: Matrix Representations of the Alexander Polynomial of a Link
Thesis Matrix Representations of Knot and Link Groups
Poster Poster

Matrix Representation of Knot and Link Groups

In Introduction aux Polynomes d'un Noeud by George de Rham a method of finding the Alexander Polynomial and elementary ideals of a knot using a homomorphism between the fundamental group of the knot and the group of similarity transforms of a plane is discussed. I intend to extend this method to be defined over links. This will involve working with fundamental groups with more conjugacy classes and a multi-variable Alexander Plynomial. Finding the appropriate group of matrices will open up new ways of looking at questions about how the Alexander Polynomials of the components of the link are related to the Alexander Polynomial of the link. Since this is an unexplored view of the link it has the possibility of opening up new questions and giving a clearer understanding of the relations in and between links.