Auslander-reiten Triangles and Quivers over Topological Spaces
نویسنده
چکیده
In this paper, Auslander-Reiten triangles are introduced into algebraic topology, and it is proved that their existence characterizes Poincaré 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.
منابع مشابه
A pr 2 00 3 THE AUSLANDER - REITEN QUIVER OF A POINCARÉ DUALITY SPACE
In a previous paper, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincaré duality space, each component of the Auslander-Reiten quiver is isomorphic to ZA∞.
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