On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes

Yoshiyasu Fukumoto

*(Kyoto University)*

10:00-11:00 am, October 19, 2016 Science Building A1510

__Abstract:__

The main result I will discuss is non-vanishing of the image of the index map from the G-equivariant K-homology of a G-manifold X to the K-theory of the C*-algebra of the group G.
The action of G on X is assumed to be proper and cocompact.
Under the assumption that the Kronecker pairing of a K-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero.
Neither discreteness of the locally compact group G nor freeness of the action of G on X are required.
The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.

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