Poincaré duality with cap products in intersection homology

Abstract : For having a Poincaré duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an additional hypothesis on the torsion. In this work, by using the classical geometric process of blowing-up, adapted to a simplicial setting, we build a cochain complex which gives a Poincaré duality via a cap product with intersection homology, for any commutative ring of coefficients. We prove also the topological invariance of the blown-up intersection cohomology with compact supports in the case of a paracompact pseudomanifold with no codimension one strata. This work is written with general perversities, defined on each stratum and not only in function of the codimension of strata. It contains also a tame intersection homology, suitable for large perversities.
Type de document :
Pré-publication, Document de travail
2017
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https://hal-univ-artois.archives-ouvertes.fr/hal-01427131
Contributeur : Martintxo Saralegi-Aranguren <>
Soumis le : jeudi 5 janvier 2017 - 12:23:15
Dernière modification le : mercredi 25 avril 2018 - 14:23:16
Document(s) archivé(s) le : jeudi 6 avril 2017 - 13:09:13

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ArxivJanvier2017.pdf
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  • HAL Id : hal-01427131, version 1

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David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré. Poincaré duality with cap products in intersection homology. 2017. 〈hal-01427131〉

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