Non-commutative multivariable Reidemester torsion and the Thurston norm

Harvey, Shelly L¹ ; Friedl, Stefan²

¹Department of Mathematics, Rice University, 6100 Main Street, MS 136, Houston TX 77005, USA
²Département de Mathématiques, UQAM, C P 8888, Succursale Centre-ville, Montréal, Qc H3C 3P8, Canada

Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 755-777

Résumé

Given a 3–manifold the second author defined functions δn: H1(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.

Détail

DOI : 10.2140/agt.2007.7.755

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

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