Singular decompositions of a cap-product

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

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Singular decompositions of a cap-product

Author(s) :

Chataur, David [Auteur]
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 UPJV [LAMFA]
Saralegi-Aranguren, Martintxo [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Tanré, Daniel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Proceedings of the American Mathematical Society

Pages :

3645-3656

Publisher :

American Mathematical Society

Publication date :

2017

ISSN :

0002-9939

HAL domain(s) :

Mathématiques [math]/Topologie algébrique [math.AT]

English abstract : [en]

In the case of a compact orientable pseudomanifold, a well-known theorem of M. Goresky and R. MacPherson says that the cap-product with a fundamental class factorizes through theintersection homology groups. In this work, ...
Show more >In the case of a compact orientable pseudomanifold, a well-known theorem of M. Goresky and R. MacPherson says that the cap-product with a fundamental class factorizes through theintersection homology groups. In this work, we show that this classical cap-product is compatiblewith a cap-product in intersection (co)-homology, that we have previously introduced. As a corollary,for any commutative ring of coefficients, the existence of a classical Poincar´e duality isomorphism isequivalent to the existence of an isomorphism between the intersection homology groups correspondingto the zero and the top perversities. Our results answer a question asked by G. Friedman.Show less >

Language :

Anglais

Popular science :

Non

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