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arXiv · 2211.04389

Torsion homology growth of polynomially growing free-by-cyclic groups

Naomi Andrew·Sam Hughes·Monika Kudlinska
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Abstract

We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodromy vanishes in every dimension independently of the choice of Farber chain. It follows that the integral torsion $\rho^\mathbb{Z}$ equals the $\ell^2$-torsion $\rho^{(2)}$ verifying a conjecture of L\"uck for these groups.

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Naomi Andrew, Sam Hughes, Monika Kudlinska. 2022-11-08. Torsion homology growth of polynomially growing free-by-cyclic groups. https://doi.org/10.1216/rmj.2024.54.933

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