Calabi-Yau categories and Poincare duality spaces

Details Calabi-Yau categories and Poincare duality spaces Calabi-Yau categories and Poincare duality spaces

2008-01-14

arxiv.org/abs/0801.2052v2

Mathematics

Representation Theory

33 pages; minor changes. To appear in the ICRA XII volume "Trends in Representation Theory of Algebras and Related Topics"

Scientific paper

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.

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