The Farrell–Jones Conjecture for Hyperbolic-by-Cyclic Groups

Abstract

We prove the Farrell–Jones conjecture (FJC) for mapping tori of automorphisms of virtually torsion-free hyperbolic groups. The proof uses recently developed geometric methods for establishing the FJC by Bartels–Lück–Reich, as well as the structure theory of mapping tori by Dahmani–Krishna.