Abstract
We establish certain ‘homological properties’ of the stable Higson corona used by Emerson and Meyer to study the Dirac-dual-Dirac approach to the Baum-Connes conjecture [5]. These are used to obtain explicit isomorphisms between the K-theory of the stable Higson corona of certain spaces X and the topological K-theory of natural geometric boundaries of X. This is sufficient to give a simple proof of the strong Novikov conjecture for torsion free hyperbolic groups and torsion free groups acting properly and cocompactly on CAT (0) spaces, and also provides an input into an index theorem in single operator theory [15, 16].
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