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 . These are used to obtain explicit isomorphisms between the K-theory groups of stable Higson coronas, and the K-theory groups of certain geometrically defined boundaries. 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 , .
Cite this article
Rufus Willett, Some ‘homological’ properties of the stable Higson corona. J. Noncommut. Geom. 7 (2013), no. 1, pp. 203–220DOI 10.4171/JNCG/114