2018/04/22 by Adam Rennie, David Robertson, Rennie, A. +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1804.08114
openalex publication_date 2018/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.