Reidemeister Torsion, the Thurston Norm and Harvey’s Invariants

Recently representations over non–commutative rings were used by Cochran, Harvey, Friedl–Kim and Turaev to define Alexander polynomials whose degrees give lower bounds on the Thurston norm. We first show how Reidemeister torsion relates to these invariants. We give lower bounds on the Thurston norm in terms of the Reidemeister torsion which contain 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.