A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds
Geometric Topology
2012-08-06 v2 Symplectic Geometry
Abstract
In this paper we show that given any 3-manifold N and any non-fibered class in H^1(N;Z) there exists a representation such that the corresponding twisted Alexander polynomial is zero. This is obtained by extending earlier work of the authors, together with results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.
Keywords
Cite
@article{arxiv.1205.2434,
title = {A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds},
author = {Stefan Friedl and Stefano Vidussi},
journal= {arXiv preprint arXiv:1205.2434},
year = {2012}
}
Comments
15 pages. Supersedes arXiv:0801.1513. This is the final version, to be published by the Journal of the European Mathematical Society