The Farrell-Hsiang method revisited

TL;DR

This paper revisits the Farrell-Hsiang method to establish a new sufficient condition for groups to satisfy the Farrell-Jones Conjecture in algebraic K- and L-theory, based on finite quotients.

Contribution

It introduces a novel criterion involving finite quotients that broadens the applicability of the Farrell-Hsiang approach to the Farrell-Jones Conjecture.

Findings

Provides a new sufficient condition for the Farrell-Jones Conjecture

Connects finite quotients of groups with the conjecture's validity

Enhances understanding of group properties related to algebraic K- and L-theory

Abstract

We present a sufficient condition for groups to satisfy the Farrell-Jones Conjecture in algebraic K-theory and L-theory. The condition is formulated in terms of finite quotients of the group in question and is motivated by work of Farrell-Hsiang.