Twisted Alexander polynomials, symplectic 4-manifolds and surfaces of   minimal complexity
  Let M be a 4-manifold which admits a free circle action. We use twisted Alexander polynomials to study the existence of symplectic structures and the minimal complexity of surfaces in M. The results on the existence of symplectic structures summarize previous results of the authors in [FV08a,FV08,FV07]. The results on surfaces of minimal complexity are new. 
Stefan Friedl and Stefano Vidussi