Peter D. Horn
Abstract: Cochran defined the nth-order integral Alexander module of a knot in the three sphere as the first homology group of the knot's (n+1)th-iterated abelian cover. The case n=0 gives the classical Alexander module (and polynomial). After a localization, one can get a finitely presented module over a principal ideal domain, from which one can extract a higher-order Alexander polynomial. We present an algorithm to compute the first-order Alexander module for any knot. Included in this algorithm is a solution to the word problem in finitely presented Z[Z]-modules.
Journal: Experimental Mathematics, Volume 23, Issue 2, 2014
DOI: 10.1080/10586458.2014.882806