Exponential growth of torsion in abelian coverings

Raimbault, Jean

doi:10.2140/agt.2012.12.1331

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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/

Volume 12, issue 3 (2012)