JournalsjncgVol. 7, No. 1pp. 203–220

Some ‘homological’ properties of the stable Higson corona

  • Rufus Willett

    Vanderbilt University, Nashville, USA
Some ‘homological’ properties of the stable Higson corona cover
Download PDF

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 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 [15], [16].

Cite this article

Rufus Willett, Some ‘homological’ properties of the stable Higson corona. J. Noncommut. Geom. 7 (2013), no. 1, pp. 203–220

DOI 10.4171/JNCG/114