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 and AR theory.
Auslander-Reiten triangles and quivers over topological spaces
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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.
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2025 1verdicts
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Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory
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 and AR theory.