Auslander-Reiten theory over topological spaces

@inproceedings{Jrgensen2004AuslanderReitenTO,
  title={Auslander-Reiten theory over topological spaces},
  author={Peter S{\o}gaard J{\o}rgensen},
  year={2004}
}
Auslander–Reiten triangles and quivers are introduced into algebraic topology. It is proved that the existence of Auslander–Reiten triangles characterizes Poincaré duality spaces, and that the Auslander–Reiten quiver is a weak homotopy invariant. The theory is applied to spheres whose Auslander–Reiten triangles and quivers are computed. The Auslander–Reiten quiver over the d-dimensional sphere turns out to consist of d−1 copies of ZA∞. Hence the quiver is a sufficiently sensitive invariant to… CONTINUE READING
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