The L2–Alexander torsion is symmetric

Dubois, Jérôme; Friedl, Stefan; Lück, Wolfgang

doi:10.2140/agt.2015.15.3599

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The $L^2$–Alexander torsion is symmetric

Jérôme Dubois, Stefan Friedl and Wolfgang Lück

Algebraic & Geometric Topology 15 (2015) 3599–3612

DOI: 10.2140/agt.2015.15.3599

Abstract

We show that the $L^{2}$ –Alexander torsion of a $3$ –manifold is a symmetric function. This can be viewed as a generalization of the symmetry of the Alexander polynomial of a knot.

Keywords

$L^2$–Alexander torsion, duality, Thurston norm, knot genus

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57Q10

References

Publication

Received: 20 November 2014

Revised: 7 April 2015

Accepted: 24 April 2015

Published: 12 January 2016

Authors

Jérôme Dubois
Laboratoire de Mathématiques UMR 6620 – CNRS Université Blaise Pascal Campus des Cézeaux BP 80026 63171 Aubière France

Stefan Friedl
Fakultät für Mathematik Universität Regensburg D-93053 Regensburg Germany

Wolfgang Lück
Mathematisches Institut Rheinische Wilhelms-Universität Bonn Endenicher Allee 60 D-53115 Bonn Germany

Volume 15, issue 6 (2015)