Geometry/Topology
The L2-Alexander torsions of 3-manifolds
Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 69-73.

The aim of this note is to introduce L2-Alexander torsions for 3-manifolds (which are generalizations of the usual Alexander polynomial and also of the L2-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 L2-Alexander torsion detects the Thurston norm. Finally we also state a symmetry formula.

Le but de cette note est d'introduire les torsions d'Alexander L2 (généralisations du polynôme d'Alexander usuel et de l'invariant d'Alexander L2 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 L2 permettent de détecter la norme de Thurston d'une variété de dimension 3 irréductible et qu'elles sont symétriques.

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DOI: 10.1016/j.crma.2014.10.012
Dubois, Jérôme 1; Friedl, Stefan 2; Lück, Wolfgang 3

1 Université Blaise Pascal – Laboratoire de Mathématiques, UMR 6620 – CNRS, Campus des Cézeaux – B.P. 80026, 63171 Aubière cedex, France
2 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
3 Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
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Dubois, Jérôme; Friedl, Stefan; Lück, Wolfgang. The $ {L}^{2}$-Alexander torsions of 3-manifolds. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 69-73. doi : 10.1016/j.crma.2014.10.012. http://www.numdam.org/articles/10.1016/j.crma.2014.10.012/

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