JournalscmhVol. 79, No. 1pp. 160–182

Auslander-Reiten theory over topological spaces

  • Peter Jørgensen

    University of Newcastle, Newcastle upon Tyne, UK
Auslander-Reiten theory over topological spaces cover
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Abstract

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 dd-dimensional sphere turns out to consist of d1d-1 copies of ZA{\mathbb Z} A_{\infty}. Hence the quiver is a sufficiently sensitive invariant to tell spheres of different dimension apart.

Cite this article

Peter Jørgensen, Auslander-Reiten theory over topological spaces. Comment. Math. Helv. 79 (2004), no. 1, pp. 160–182

DOI 10.1007/S00014-001-0795-4