Simlpicial intersection homology revisited

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

Document type :

Pré-publication ou Document de travail

Title :

Simlpicial intersection homology revisited

Author(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]

Publication date :

2021-09-01

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Comment :

26 poages, 3 figures

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2109.00261
Open access
Access the document

Simlpicial intersection homology revisited BibTeX CSV Excel RIS

Files

Simlpicial intersection homology revisited

BibTeX

CSV

Excel

RIS