Volume 12, issue 3 (2012)

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Exponential growth of torsion in abelian coverings

Jean Raimbault

Algebraic & Geometric Topology 12 (2012) 1331–1372
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