Auslander-Reiten triangles and quivers over topological spaces

Details Auslander-Reiten triangles and quivers over topological spaces Auslander-Reiten triangles and quivers over topological spaces

2003-04-06

arxiv.org/abs/math/0304079v1

Mathematics

Algebraic Topology

25 pages

Scientific paper

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_{\infty}. So quivers are sufficiently sensitive invariants to tell spheres of different dimension apart.

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