Algebraic & Geometric Topology

Non-commutative multivariable Reidemester torsion and the Thurston norm

Shelly L Harvey and Stefan Friedl

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Given a 3–manifold the second author defined functions δn:H1(M;), 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.

Article information

Algebr. Geom. Topol., Volume 7, Number 2 (2007), 755-777.

Received: 18 August 2006
Accepted: 16 April 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx]

Thurston norm 3–manifolds Alexander norm Dieudonné determinant


Harvey, Shelly L; Friedl, Stefan. Non-commutative multivariable Reidemester torsion and the Thurston norm. Algebr. Geom. Topol. 7 (2007), no. 2, 755--777. doi:10.2140/agt.2007.7.755.

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