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.