Exponential growth of torsion in Abelian coverings

Abstract

We study the growth of the order of torsion subgroups of the homology in a tower of finite abelian coverings. In particular, we prove that it is exponential for when the tower converges to the maximal free abelian cover of a link complement when the first nonzero Alexander polynomial has positive logarithmic Mahler measure.

42 pages, to appear in AGT. Various minor mistakes corrected and exposition changed

References in corpus (2)

• The cobordism group of homology cylinders
• Homology torsion growth and Mahler measure

Cited by in corpus (15)

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• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
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• Survey on approximating L^2-invariants by their classical counterparts: Betti numbers, torsion invariants and homological growth
• Convergence to the Mahler measure and the distribution of periodic points for algebraic Noetherian ${\mathbb{Z}}^d$-actions
• Three flavors of twisted invariants of knots
• Approximations to the volume of hyperbolic knots
• Homology torsion growth and Mahler measure
• Torsion homology growth beyond asymptotics
• Torsion in the homology of finite covers of 3-manifolds
• Limits of Mahler measures in multiple variables
• Some non-abelian covers of knots with non-trivial Alexander polynomial
• Growth of regulators in finite abelian coverings
• Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds
• Examples of homological torsion and volume growth