## Geometry Seminar - Abstracts

### Talk

Tuesday 4 July 2017, 16:00-17:00 in HG03.085

**Adam Rennie** (University of Wollongong)

*Poincare duality for some Cuntz-Pimsner algebras*

### Abstract

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.

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