Non-commutative multivariable Reidemester torsion and the Thurston norm

Harvey, Shelly L; Friedl, Stefan

doi:10.2140/agt.2007.7.755

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Non-commutative multivariable Reidemester torsion and the Thurston norm

Shelly Harvey and Stefan Friedl

Algebraic & Geometric Topology 7 (2007) 755–777

DOI: 10.2140/agt.2007.7.755

Abstract

Given a 3–manifold the second author defined functions $δ_{n} : H^{1} (M; ℤ) \to ℕ$ , 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.

Keywords

Thurston norm, 3–manifolds, Alexander norm, Dieudonné determinant

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57N10

References

Publication

Received: 18 August 2006

Accepted: 16 April 2007

Published: 30 May 2007

Authors

Shelly Harvey
Department of Mathematics Rice University 6100 Main Street MS 136 Houston TX 77005 USA

Stefan Friedl
Département de Mathématiques UQAM C P 8888, Succursale Centre-ville Montréal, Qc H3C 3P8 Canada

Volume 7, issue 2 (2007)