TORSION HOMOLOGY GROWTH OF POLYNOMIALLY GROWING FREE-BY-CYCLIC GROUPS

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 Lück for these groups.