Non-commutative Multivariable Reidemeister Torsion and the Thurston Norm

Stefan Friedl; Shelly Harvey

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arXiv · math/0608409

Non-commutative Multivariable Reidemeister Torsion and the Thurston Norm

Stefan Friedl·Shelly Harvey

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Abstract

In a previous paper, the second author defined integer-valued functions delta_n on the first cohomology of a 3-manifold, generalizing McMullen's Alexander norm. It was shown that these functions give lower bounds on the Thurston norm. In this paper, 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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Stefan Friedl, Shelly Harvey. 2006-08-16. Non-commutative Multivariable Reidemeister Torsion and the Thurston Norm. https://arxiv.org/abs/math/0608409

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