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arXiv · 1804.08114

Poincare duality for Cuntz-Pimsner algebras of bimodules

A. Rennie·D. Robertson·A. Sims
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Abstract

We present a new approach to Poincare duality for Cuntz-Pimsner algebras. We provide sufficient conditions under which Poincare self-duality for the coefficient algebra of a Hilbert bimodule lifts to Poincare 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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BibTeXRIS

A. Rennie, D. Robertson, A. Sims. 2018-04-22. Poincare duality for Cuntz-Pimsner algebras of bimodules. https://arxiv.org/abs/1804.08114

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