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Auslander-Reiten triangles and quivers over topological spaces

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arxiv math/0304079 v1 pith:RXZLN4SN submitted 2003-04-06 math.AT math.RAmath.RT

Peter Jorgensen This is my paper · ORCID
classification math.ATmath.RAmath.RT
keywords quiversauslander-reitentrianglesintroducedinvariantsspacesspheresalgebraic
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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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    The paper constructs infinite discrete Nakayama representations via persistence theory and stabilizes them into negative Calabi-Yau versions of Igusa-Todorov discrete cluster categories of type A, with geometric model...

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