2003/04/06 by Peter Jørgensen, Peter Jorgensen, Jorgensen, Peter
Mathematics · #16E45 #16G70 #55P62 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AT #math.RA #math.RT #msc:16E45 #msc:16G70 #msc:55P62
paper · pdf · doi:10.48550/arxiv.math/0304079
25 pages
arxiv created 2003/04/06 · openalex publication_date 2003/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∞. So quivers are sufficiently sensitive invariants to tell spheres of different dimension apart.