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

2016/04/02 by Fukumoto, Yoshiyasu
#19K35 #19K56 #46L80 #57R20 #58A12 #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1604.00464

Abstract

The main result of this paper is non-vanishing of the image of the index map from the G-equivariant K-homology of a proper G-compact G-manifold X to the K-theory of the C^*-algebra of the group G. 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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