Baum-Connes conjecture

• The Baum-Connes conjecture, stated in 1982 [P. F. Baum and A. Connes, Enseign. Math. (2) 46 (2000), no. 1-2, 3–42; MR1769535], is a daring assertion identifying the K-theory of a group C∗-algebra, be it a discrete group or a Lie group (or the C∗-algebra of a foliation), and a topological group of equivariant indices.