In the early 2000's Cochran and Harvey introduced non-commutative Alexander
polynomials for 3-manifolds. Their degrees give strong lower bounds on the
Thurston norm. In this paper we make the case that the vanishing of a certain
Novikov-Sikorav homology module is the correct notion of a monic
non-commutative Alexander polynomial. Furthermore we will use the opportunity
to give new proofs of several statements about Novikov-Sikorav homology in the
three-dimensional context.Comment: 30 pages, to appear in a special volume of JKTR in memory of Tim
Cochra
