Algebraic & Geometric Topology

Exponential growth of torsion in abelian coverings

Jean Raimbault

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1331-1372.

Received: 8 April 2011
Revised: 24 February 2012
Accepted: 20 March 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M10: Covering spaces
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]

Reidemeister torsion $\ell^2$–torsion


Raimbault, Jean. Exponential growth of torsion in abelian coverings. Algebr. Geom. Topol. 12 (2012), no. 3, 1331--1372. doi:10.2140/agt.2012.12.1331.

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