On the Farrell-Jones and related Conjectures

TL;DR

This paper provides an introductory overview of the Farrell-Jones and Baum-Connes Conjectures, discussing their significance and related topics in algebraic K-theory and group cohomology.

Contribution

It offers a comprehensive introduction to these conjectures, summarizing key ideas and recent developments based on lectures from a summer school.

Findings

Summarizes the status of the Farrell-Jones and Baum-Connes Conjectures.

Highlights connections between algebraic K-theory and group cohomology.

Provides insights into ongoing research and open problems.

Abstract

These extended notes are based on a series of six lectures presented at the summer school ``Cohomology of groups and algebraic $K$-theory'' which took place in Hangzhou, China from July 1 until July 12 in 2007. They give an introduction to the Farrell-Jones and the Baum-Connes Conjecture.