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Poincare duality for Cuntz-Pimsner algebras of bimodules

Journal Article


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.

Publication Date


  • 2018

Citation


  • Rennie, A., Robertson, D., & Sims, A. (2018). Poincare duality for Cuntz-Pimsner algebras of bimodules. Retrieved from http://arxiv.org/abs/1804.08114v1

Web Of Science Accession Number


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.

Publication Date


  • 2018

Citation


  • Rennie, A., Robertson, D., & Sims, A. (2018). Poincare duality for Cuntz-Pimsner algebras of bimodules. Retrieved from http://arxiv.org/abs/1804.08114v1

Web Of Science Accession Number