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Comptes Rendus Mathématique
Volume 353, n° 1
pages 69-73 (janvier 2015)
Doi : 10.1016/j.crma.2014.10.012
Received : 19 August 2014 ;  accepted : 16 October 2014
The  -Alexander torsions of 3-manifolds
Torsions d'Alexander   pour les variétés de dimension trois
 

Jérôme Dubois a , Stefan Friedl b , Wolfgang Lück c
a Université Blaise Pascal – Laboratoire de Mathématiques, UMR 6620 – CNRS, Campus des Cézeaux – B.P. 80026, 63171 Aubière cedex, France 
b Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany 
c Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany 

Abstract

The aim of this note is to introduce  -Alexander torsions for 3-manifolds (which are generalizations of the usual Alexander polynomial and also of the  -Alexander invariant defined by Li and Zhang [[7]]) and to report on calculations for graph manifolds and fibered 3-manifolds. We further announce that given any irreducible 3-manifold, there exists a coefficient system such that the corresponding  -Alexander torsion detects the Thurston norm. Finally we also state a symmetry formula.

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Résumé

Le but de cette note est d'introduire les torsions d'Alexander   (généralisations du polynôme d'Alexander usuel et de l'invariant d'Alexander   défini par Li et Zhang [[7]]) et d'en donner le calcul pour les variétés graphées et les variétés fibrées de dimension 3. On annonce enfin que les torsions d'Alexander   permettent de détecter la norme de Thurston d'une variété de dimension 3 irréductible et qu'elles sont symétriques.

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© 2014  Published by Elsevier Masson SAS de la part de Académie des sciences.
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