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.

Final version accepted for publication

References in corpus (2)

• Minimal volume entropy of simplicial complexes
• Free-by-cyclic groups, automorphisms and actions on nearly canonical trees

Cited by in corpus (2)

• Free-by-cyclic groups are equationally Noetherian
• Problems on handlebody groups