## Algebraic & Geometric Topology

### Non-commutative multivariable Reidemester torsion and the Thurston norm

#### Abstract

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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796704

Digital Object Identifier
doi:10.2140/agt.2007.7.755

Mathematical Reviews number (MathSciNet)
MR2308963

Zentralblatt MATH identifier
1147.57014

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796704

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