K-theory and actions on Euclidean retracts

TL;DR

This paper reviews axiomatic approaches to the Farrell-Jones Conjecture, focusing on actions on Euclidean retracts and their implications for groups like GL_n(Z), hyperbolic groups, and mapping class groups.

Contribution

It synthesizes axiomatic results connecting actions on Euclidean retracts with the Farrell-Jones Conjecture and explores applications to various important classes of groups.

Findings

Axiomatic frameworks for the Farrell-Jones Conjecture

Applications to GL_n(Z), hyperbolic groups, and mapping class groups

Insights into group actions on Euclidean retracts

Abstract

This note surveys axiomatic results for the Farrell-Jones Conjecture in terms of actions on Euclidean retracts and applications of these to GL_n(Z), relative hyperbolic groups and mapping class groups.