Auslander-Reiten triangles and quivers over topological spaces
Abstract
Description
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.
25 pages
25 pages