  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 Poincare duality space gives rise to a Calabi-Yau category. This paper is
a review of the theory.
