2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158632The 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.33 pages; minor changes. To appear in the ICRA XII volume "Trends in Representation Theory of Algebras and Related Topics"Representation TheoryAlgebraic TopologyRings and Algebras16E45, 16G70, 55P62text