On the Farrell-Jones Conjecture for algebraic K-theory of spaces: the Farrell-Hsiang method

TL;DR

This paper proves the Farrell-Jones Conjecture for algebraic K-theory of spaces specifically for virtually poly-Z-groups by adapting the Farrell-Hsiang method to a new categorical setting.

Contribution

It extends the Farrell-Hsiang method from linear groups to categories of equivariant, controlled retractive spaces, establishing the conjecture for a new class of groups.

Findings

Proves the Farrell-Jones Conjecture for virtually poly-Z-groups.

Adapts the Farrell-Hsiang method to categorical settings.

Establishes new techniques for algebraic K-theory of spaces.

Abstract

We prove the Farrell-Jones Conjecture for algebraic K-theory of spaces for virtually poly-Z-groups. For this, we transfer the 'Farrell-Hsiang method' from the linear case to categories of equivariant, controlled retractive spaces.