Poincar\'e duality and degrees of twisted Alexander polynomials
  We prove duality theorems for twisted Reidemeister torsions and twisted Alexander polynomials generalizing the results of Turaev. As a corollary we determine the parity of the degrees of twisted Alexander polynomials of 3-manifolds in many cases. 
Stefan Friedl, Taehee Kim and Takahiro Kitayama
math.GT