A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds

@article{Friedl2012AVT,
  title={A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds},
  author={Stefan Friedl and Stefano Vidussi},
  journal={arXiv: Geometric Topology},
  year={2012}
}
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.