English

Novikov homology, twisted Alexander polynomials and Thurston cones

Geometric Topology 2014-05-09 v1 Differential Geometry

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.

Cite

@article{arxiv.math/0406498,
  title  = {Novikov homology, twisted Alexander polynomials and Thurston cones},
  author = {A. Pajitnov},
  journal= {arXiv preprint arXiv:math/0406498},
  year   = {2014}
}

Comments

38 pages, Latex file