Date of Award
Doctor of Philosophy
James R. Conant
Morwen Thistlethwaite, Nikolay Brodskiy, Michael Berry
The Conant's conjecture  which has foundation on the Conway polynomial and Vassiliev invariants is the main theme of this research. The Conant's conjecture claim that the Conway polynomial of amphicheiral knots split over integer modulo 4 space. We prove Conant's conjecture for amphicheiral knots coming from braid closure in certain way. We give several counter examples to a conjecture of A. Stoimenow  regarding the leading coefficient of the Conway polynomial. We also construct integer bases for chord diagrams up to order 7 and up to order 6 for Vassiliev invariants. Finally we develop a method to extract integer valued Vassiliev invariants from coefficients of the Jones polynomial.
Manathunga, Vajira Asanka, "The Conway Polynomial and Amphicheiral Knots. " PhD diss., University of Tennessee, 2016.