Auslander-Reiten triangles and quivers over topological spaces
Abstract
In this paper, Auslander-Reiten triangles are introduced into algebraic topology, and it is proved that their existence characterizes Poincare duality spaces. Invariants in the form of quivers are also introduced, and Auslander-Reiten triangles and quivers over spheres are computed. The quiver over the d-dimensional sphere turns out to consist of d-1 components, each isomorphic to ZA∞. So quivers are sufficiently sensitive invariants to tell spheres of different dimension apart.
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