Calabi–Yau categories and Poincaré duality

Abstract

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.