Auslander-Reiten triangles and quivers over topological spaces
Algebraic Topology
2007-05-23 v1 Rings and Algebras
Representation Theory
Abstract
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.
Cite
@article{arxiv.math/0304079,
title = {Auslander-Reiten triangles and quivers over topological spaces},
author = {Peter Jorgensen},
journal= {arXiv preprint arXiv:math/0304079},
year = {2007}
}
Comments
25 pages