Novikov homology, twisted Alexander polynomials and Thurston cones
A. Pajitnov
Abstract
We continue the study of the twisted Novikov homology, introduced in our joint paper with H.Goda (arXiv:math.DG/0312374), and its generalizations. The main applications of the developed algebraic techniques are to the topology of 3-manifolds. We show in particular that the twisted Novikov homology of a 3-manifold M of zero Euler characteristic vanishes if and only if the corresponding twisted Alexander polynomial of the fundamental group of M is monic. We discuss the relations between the Thurston norm on 1-cohomology of a three-dimensional manifold and the twisted Novikov homology of this manifold.
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