EXPANDERS AND K-THEORY FOR GROUP C* ALGEBRAS
Speaker: Paul Baum, Penn State
Abstract: An expander or expander family is a sequence of finite graphs X_1, X_2, X_3, ... which is efficiently connected. A discrete group G which``contains" an expander in its Cayley graph is a counter-example to the Baum-Connes (BC) conjecture with coefficients. Some care must be taken with the definition of ``contains". M. Gromov outlined a method for constructing such a group. G. Arjantseva and T. Delzant completed the construction. The group so obtained is known as the Gromov group and is the only known example of a non-exact group. The left side of BC with coefficients ``sees" any group as if the group were exact. This talk will indicate how to make a change in the right side of BC with coefficients so that the right side also ``sees" any group as if the group were exact. This corrected form of BC with coefficients uses the unique minimal exact and Morita compatible intermediate crossed-product. For exact groups (i.e. all groups except the Gromov group) there is no change in BC with coefficients. In the corrected form of BC with coefficients, the Gromov group acting on the coefficient algebra obtained from the expander is not a counter-example. Thus at the present time (January , 2014) there is no known counter-example to the corrected form of BC with coefficients. The above is joint work E. Guentner and R. Willett. This work is based on --- and inspired by --- a result of R. Willett and G. Yu.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm