Let G be a (countable) discrete group. C*r(G) denotes the reduced C* algebra of G. The BC (Baum-Connes) conjecture proposes an answer to the problem of calculating the K-theory of C*r(G). This talk states the conjecture from the point of view of index theory. The Atiyah-Singer index theorem then appears as the special case when the group G is the trivial one-element group. For a general (countable) discrete group G, the Chern character (on the left side of the conjecture) is obtained by writing down the Atiyah-Singer formula for the index of the appropriate Dirac operator.
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Last updated 15 April 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).