  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.
