Dirac operator and K-theory for discrete groups

Paul Baum (Pennsylvania State University)

Tuesday 5th May, 2009 16:15-17:15 Mathematics Building, room 204


Let G be a (countable) discrete group. By using the regular representation of G, the purely algebraic complex group algebra can be completed to obtain a C* algebra known as the reduced C* algebra of G. Various problems in geometry-topology (e.g. Novikov higher signature conjecture, Gromov- Lawson-Rosenberg positive scalar curvature conjecture) hinge on understanding the K-theory of this C* algebra. The BC (Baum-Connes) conjecture proposes a formula for this K-theory. This talk will review the definition of K-theory for C* algebras, and will then explain BC from a point of view which is very closely connected to elliptic operators and the Atiyah-Singer index theorem. Equivariant Chern character will play a role.

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