Tuesday 4 July 2017, 16:00-17:00 in HG03.085
Adam Rennie (University of Wollongong)
Poincare duality for some Cuntz-Pimsner algebras
A Cuntz-Pimsner algebra describes the crossed product of an algebra A by aa A bimodule E. We find sufficient conditions for Poincare duality classes for the algebra A to lift to the Cuntz-Pimsner algebra. We then show how for a very wide class of Cuntz-Pimsner algebras we can obtain the K-theory fundamental class, using a construction of Arici and R. The K-homology fundamental class is more difficult, but we show how to recover Kaminker and Putnam's fundamental class for Cuntz-Krieger algebras, and much more general graph algebras. We also obtain a fundamental class for crossed products of spin manifolds by isometries.