Mathematical Sciences: K-Theory for Operator Algebras, Index Theory, Riemann-Roch

9401440 Baum The BC (= Baum-Connes) conjecture is an extremely general equality relating topology, i.e. continuous geometry, and analysis, i.e. the branch of mathematics based on multi-variable calculus. This conjecture is unusual in that it cuts across several different areas of mathematics and thus reveals an underlying unity which previously was completely unknown. The research pursued here centers on proving this conjecture for certain classes of examples and then obtaining corollaries. More precisely, let G be a topological group which is Hausdorff, locally compact and second countable. The main examples are Lie groups, p-adic groups and discrete groups. C*G denotes the reduced C*-algebra of G, and KC*G is its K-theory. The BC conjecture, if true, gives an answer to the problem of calculating KC*G. Validity of the conjecture has applications to well-known problems in geometry-topology and representation theory. ***