#### Volume 7, issue 2 (2007)

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 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Non-commutative multivariable Reidemester torsion and the Thurston norm

### Shelly Harvey and Stefan Friedl

Algebraic & Geometric Topology 7 (2007) 755–777
##### Abstract

Given a 3–manifold the second author defined functions ${\delta }_{n}:{H}^{1}\left(M;ℤ\right)\to ℕ$, 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
Primary: 57M27
Secondary: 57N10