Simlpicial intersection homology revisited

Chataur, David; Saralegi-Aranguren, Martin; Tanré, Daniel

Type de document :

Pré-publication ou Document de travail

Titre :

Simlpicial intersection homology revisited

Auteur(s) :

Chataur, David [Auteur]
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 UPJV [LAMFA]
Saralegi-Aranguren, Martin [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Tanré, Daniel [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Date de publication :

2021-09-01

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Intersection homology is defined for simplicial, singular and PL chains. In the case of a filtered simplicial complex, it is well known that the three versions are isomorphic. This isomorphism is established by using the ...
Lire la suite >Intersection homology is defined for simplicial, singular and PL chains. In the case of a filtered simplicial complex, it is well known that the three versions are isomorphic. This isomorphism is established by using the PL case as an intermediate between the singular and the simplicial situations. Here, we give a proof similar to the classical proof for ordinary simplicial complexes. We also study the intersection blown-up cohomology that we have previously introduced. In the case of a pseudomanifold, this cohomology owns a Poincar\'e isomorphism with the intersection homology, for any coefficient ring, thanks to a cap product with a fundamental class. We prove that the simplicial and the singular blown-up cohomologies of a filtered simplicial complex are isomorphic. From this result, we can now compute the blown-up intersection cohomology of a pseudomanifold from a triangulation. Finally, we introduce a blown-up intersection cohomology for PL-spaces and prove that it is isomorphic to the singular ones. We also show that the cup product in perversity $ \overline 0$ of a CS-set coincides with the cup product of the singular cohomology of the underlying topological space.Lire moins >

Langue :

Anglais

Commentaire :

26 poages, 3 figures

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

2109.00261
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