On the transfer reducibility of certain Farrell-Hsiang groups

TL;DR

This paper improves the proof of the Farrell-Jones Conjecture for virtually poly-Z groups by demonstrating that transfer reducibility, combined with inheritance properties, suffices for the conjecture's validity.

Contribution

It refines existing proofs by showing transfer reducibility alone, along with inheritance properties, is enough to establish the Farrell-Jones Conjecture for certain groups.

Findings

Proof of Farrell-Jones Conjecture now relies solely on transfer reducibility and inheritance properties.

Enhanced understanding of the conditions under which the conjecture holds for virtually poly-Z groups.

Simplification of the proof process for this class of groups.

Abstract

We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for the validity of the conjecture.