Coarse geometric approach to the Baum-Connes conjecture

Dr. Dapeng Zhou

*(Vanderbilt University)*

10:00 am to 11:00 am, Mar 13th, 2014 Science Building A1510

__Abstract:__

For a proper cocompact $G$-space $X$, the assembly map in the Baum-Connes conjecture identifies two object associated with $G$, one analytical and one geometrical/topological.
We can also form an equivariant Roe algebra associated to the coarse geometry of the $G$-space $X$.

The assembly map defined by coarse geometry can be identified with the original one defined by $KK$-theory. When the action is not cocompact, we can still form a coarse geometric index which has no known counterpart in the $KK$-theoretic approach. This is still uncharted territory to explore.

The assembly map defined by coarse geometry can be identified with the original one defined by $KK$-theory. When the action is not cocompact, we can still form a coarse geometric index which has no known counterpart in the $KK$-theoretic approach. This is still uncharted territory to explore.

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