Volume 7, issue 2 (2007)

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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
Abstract

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.

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