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Poincare duality for Cuntz–Pimsner algebras

Journal Article


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.

Publication Date


  • 2019

Citation


  • Rennie, A., Robertson, D. & Sims, A. (2019). Poincare duality for Cuntz–Pimsner algebras. Advances in Mathematics, 347 1112-1172.

Scopus Eid


  • 2-s2.0-85063029528

Number Of Pages


  • 60

Start Page


  • 1112

End Page


  • 1172

Volume


  • 347

Place Of Publication


  • United Kingdom

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.

Publication Date


  • 2019

Citation


  • Rennie, A., Robertson, D. & Sims, A. (2019). Poincare duality for Cuntz–Pimsner algebras. Advances in Mathematics, 347 1112-1172.

Scopus Eid


  • 2-s2.0-85063029528

Number Of Pages


  • 60

Start Page


  • 1112

End Page


  • 1172

Volume


  • 347

Place Of Publication


  • United Kingdom