Poincare duality for Cuntz-Pimsner algebras

Authors

Adam C. Rennie, University of WollongongFollow
David I. Robertson, University of NewcastleFollow
Aidan Sims, University of WollongongFollow

RIS ID

134172

Publication Details

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

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.

Grant Number

ARC/DP120100507