  Recently twisted and higher order Alexander polynomials were used by Cochran,
Harvey, Friedl--Kim and Turaev to give lower bounds on the Thurston norm. We
first show how Reidemeister torsion relates to these Alexander polynomials. We
then give lower bounds on the Thurston norm in terms of the Reidemeister
torsion which contain and extend all the above lower bounds and give an elegant
reformulation of the bounds of Cochran, Harvey and Turaev. The Reidemeister
torsion approach also gives a natural approach to proving and extending certain
monotonicity results of Cochran and Harvey.
