Vol. 230, No. 2, 2007

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ISSN: 0030-8730
Reidemeister torsion, the Thurston norm and Harvey’s invariants

Stefan Friedl

Vol. 230 (2007), No. 2, 271–296
Abstract

Cochran introduced Alexander polynomials over noncommutative Laurent polynomial rings. Their degrees were studied by Cochran, Harvey and Turaev, who gave lower bounds on the Thurston norm. We extend Cochran’s definition to twisted Alexander polynomials, and show how Reidemeister torsion relates to these invariants, giving lower bounds on the Thurston norm in terms of the Reidemeister torsion. This yields a concise formulation of the bounds of Cochran, Harvey and Turaev. The Reidemeister torsion approach also provides a natural approach to proving and extending certain monotonicity results of Cochran and Harvey.

Keywords
Thurston norm, Reidemeister torsion, 3-manifolds, knot genus
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57N10
Milestones
Received: 31 August 2005
Revised: 13 December 2005
Published: 1 April 2007
Authors
Stefan Friedl
Département de mathématiques
UQAM
C.P. 8888, Succursale Centre-ville
Montréal, Qc H3C 3P8
Canada
http://www.labmath.uqam.ca/~friedl/index.html