The Conway Polynomial and Amphicheiral Knots

The Conant's conjecture [7] 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 [32] 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.