2024/12/08 by Yuan Gao, Gao, Yuan
Computer Science · Mathematics · #18G70 #53D37 #55U30 #Advanced Graph Theory Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2412.05927
openalex publication_date 2024/12/08 · openalex created_date 2024/12/12 · openalex updated_date 2026/07/28
Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincaré-Lefschetz duality of dimension n has a boundary which itself satisfies Poincaré duality of dimension n, we show that the categorical formal punctured neighborhood of infinity, a canonical categorical construction associated to every A∞ category, has a weak proper Calabi-Yau structure of dimension n-1 whenever the original A∞ category admits a weak smooth Calabi-Yau structure of dimension n. Applications include proper Calabi-Yau structures on Rabinowitz Fukaya category of a Liouville manifold and Orlov's singularity category of a proper singular Gorenstein scheme of finite type.