Let G be a topological group which is locally compact, Hausdorff, and second countable. Examples are Lie groups, p-adic groups, adelic groups, and discrete groups. Using the (left) regular representation of G, a C*-algebra is
constructed which is known as the reduced C*-algebra of G. In 1980,
P.Baum and A.Connes conjectured an answer for the problem of calculating the K-theory of this C*-algebra. When true, the conjecture has several corollaries. This talk will state the conjecture and will briefly indicate the corollaries.
The talk is intended for non-specialists, so the basic
definitions (C*-algebra, K-theory etc.) will be carefully stated. |