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

TL;DR

This paper proves the Farrell-Jones Conjecture for a class of groups formed by automorphisms of hyperbolic groups, using advanced geometric and structural methods.

Contribution

It extends the Farrell-Jones Conjecture to hyperbolic-by-cyclic groups, combining recent geometric techniques with the structure theory of mapping tori.

Findings

Proves the Farrell-Jones Conjecture for hyperbolic-by-cyclic groups.

Utilizes geometric methods by Bartels-Lück-Reich.

Incorporates structure theory of mapping tori by Dahmani-Krishna.

Abstract

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.