On the Farrell-Jones and related Conjectures

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.

💡 Research Summary

The six‑lecture notes compiled in this paper serve as a comprehensive introduction to two of the most influential conjectures in modern topology and non‑commutative geometry: the Farrell–Jones Conjecture (FJC) and the Baum–Connes Conjecture (BCC). The author begins by recalling the basic objects of algebraic K‑theory and L‑theory, emphasizing the role of the group ring ℤG and the associated assembly map, which transports homological information from the classifying space BG to the K‑theory of ℤG. The Farrell–Jones conjecture asserts that for any group G, the assembly map \