The Farrell-Jones Conjecture for hyperbolic-by-cyclic groups

We prove the Farrell-Jones Conjecture for mapping tori of automorphisms of virtually torsion-free hyperbolic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture by Bartels-L{u}ck-Reich, as well as the structure theory of mapping tori by Dahmani-Krishna.