Reidemeister torsion, the Thurston norm and Harvey's invariants

Details Reidemeister torsion, the Thurston norm and Harvey's invariants Reidemeister torsion, the Thurston norm and Harvey's invariants

2005-08-31

arxiv.org/abs/math/0508648v3

Mathematics

Geometric Topology

Final version, to be published by the Pacific Journal of Mathematics

Scientific paper

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.

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