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Pré-publication, Document de travail

A Simplicial approach to the Sheaf Theoretic construction of Intersection Cohomology

Abstract : Intersection (co)homology is a way to enhance classical (co)homology, allowing us to use a famous result called Poincaré duality on a large class of spaces known as stratified pseudomanifolds. There is a theoretically powerful way to arrive at intersection (co)homology by a classifying sheaves that satisfy what are called the Deligne axioms. There is a successful way to construct a simplicial intersection (co)homology, exposed in the works of D. Chataur, D. Tanré and M. Saralegi-Araguren, but a simplicial manifestation of the Deligne axioms has remained under shadows until now. This paper draws on constructions made by these authors, showing a simplicial manifestation of the Deligne axioms. This consists on presenting categories of "simplicial sheaves", localizing them appropriately and then stating "simplicial Deligne axioms". All this for different simplicial structures one can encounter. We finalize by presenting sheaves that satisfy the axioms on simplicial complexes.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-03383672
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Soumis le : lundi 18 octobre 2021 - 16:18:40
Dernière modification le : samedi 23 octobre 2021 - 04:09:45

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  • HAL Id : hal-03383672, version 1

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Sebastian Cea. A Simplicial approach to the Sheaf Theoretic construction of Intersection Cohomology. 2021. ⟨hal-03383672⟩

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