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Exponential growth of torsion in abelian coverings

Jean Raimbault
Algebraic & Geometric Topology 12 (2012) 1331–1372
DOI: 10.2140/agt.2012.12.1331
Abstract

We show exponential growth of torsion numbers for links whose first nonzero Alexander polynomial has positive logarithmic Mahler measure. This extends a theorem of Silver and Williams to the case of a null first Alexander polynomial and provides a partial solution for a conjecture of theirs.

Keywords
Reidemeister torsion, $\ell^2$–torsion
Mathematical Subject Classification 2000
Primary: 57M10
Secondary: 57M25, 57Q10
References
Publication
Received: 8 April 2011
Revised: 24 February 2012
Accepted: 20 March 2012
Published: 23 June 2012
Authors
Jean Raimbault
Institut de mathématiques de Jussieu
4, place Jussieu
Case 247
75252 Paris Cédex 5
France
http://www.math.jussieu.fr/~raimbault/