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(a) Setting (cid:7) X 12 = (cid:7) X 1 × (cid:7) X 2 , the pair ( X 12 , (cid:7) X 12 ) is a b-analytic manifold
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Proof (i) The map χ loc takes its values in CF ( X ∞ ) . Indeed, for F ∈ D b R c ( k X ∞ ) , χ loc ( F ) = j ∗ X (χ loc ( j X ! F )
Proof (a) Since X is subanalytic in (cid:7) X , X × X is subanalytic in (cid:7) X × (cid:7) X , and (cid:5) X = X × X ∩ (cid:5) (cid:7) is subanalytic in (cid:7) X × (cid:7) X
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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
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We introduce the category of b-analytic manifolds, a natural tool to define constructible sheaves and functions up to infinity. We study with some details the operations on these objects and also recall the Radon transform for constructible functions.
Journal of Applied and Computational Topology – Springer Journals
Published: Dec 1, 2023
Keywords: Constructible sheaves; Constructible functions; Subanalytic geometry; Radon transform; 55N99; 32B20; 32S60
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