Calabi-Yau categories and Poincaré duali- ty spaces

The singular cochain complex of a topological space is a classical object. It is a Differential Graded algebra which has been studied intensively with a range of methods, not least within rational homotopy theory. More recently, the tools of Auslander-Reiten theory have also been applied to the singular cochain complex. One of the highlights is that by these methods, each Poincaré duality space gives rise to a Calabi-Yau category. This paper is a review of the theory. Mathematics Subject Classification (2000). Primary 16E45, 16G70, 55P62.