Abstract
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.With these conditions in hand, we can constructively produce fundamental classes in K-theory for a wide range of examples. We can also produce K-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.
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