Poincaré duality for Cuntz-Pimsner algebras

Abstract

<p>We present a new approach to Poincaré duality for Cuntz-Pimsner algebras. We provide sufficient conditions under which Poincaré self-duality for the coefficient algebra of a Hilbert bimodule lifts to Poincaré self-duality for the associated Cuntz-Pimsner algebra.<br/>With these conditions in hand, we can constructively produce fundamental classes in <i>K</i>-theory for a wide range of examples. We can also produce <i>K</i>-homology fundamental classes for the important examples of Cuntz-Krieger algebras (following Kaminker-Putnam) and crossed products of manifolds by isometries, and their non-commutative analogues.</p>