m at h . G T ] 3 1 A ug 2 00 5 REIDEMEISTER TORSION , THE THURSTON NORM AND HARVEY ’ S INVARIANTS STEFAN
نویسنده
چکیده
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.
منابع مشابه
Non–commutative Multivariable Reidemeister Torsion and the Thurston Norm
Given a 3–manifold the second author defined functions δn : H (M ;Z) → N, generalizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non– commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.
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