English (United States)
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 de&amp;#64257;ne an in&amp;#64257;nite sequence of integer invariants, &amp;#948;n for (n &amp;#8805; 0), based on the derived series of fundamental groups of knot complements. While these &amp;#948;n 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 &amp;#948;1 , and then discuss an implementation of a computer program that calculates &amp;#948;1 .
Holum, Erik Robert, "Calculating the Degree of Higher Order Alexander Polynomials" (2010). Honors Theses - All. Paper 504.
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