The conjecture, if true, would have some older famous conjectures as consequences. For instance, the surjectivity part implies the Kadison–Kaplansky conjecture for a discrete torsion-free group, and the injectivity is closely related to the Novikov conjecture.
The origins of the conjecture go back to Fredholm theory, the Atiyah–Singer index theorem and the interplay of geometry with operator K-theory as expressed in the works of Brown, Douglas and Fillmore, among many other motivating subjects.
From Wikipedia, the free encyclopedia
- Introduction to the Baum-Connes Conjecture Alain VALETTE (PDF)
- A Survey on the Baum-Connes Conjecture (PDF)