Calculating the Degree of Higher Order Alexander Polynomials

Given two knots, K1 and K2 , a fundamental problem in low dimensional topology is determining if K1 and K2 are equivalent. Knot invariants are a key tool in determining this equivalence. We define an infinite sequence of integer invariants, δn for (n ≥ 0), based on the derived series of fundamental groups of knot complements. While these δn are useful, calculating them is a non- trivial task, usually requiring manipulations of modules over non-commutative, non-principal ideal domains. We detail the process of evaluating δ1 , and then discuss an implementation of a computer program that calculates δ1 .