2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67001In 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_{\infty}. So quivers are sufficiently sensitive invariants to tell spheres of different dimension apart.25 pagesAlgebraic TopologyRings and AlgebrasRepresentation Theory55P62; 16E45; 16G70text