Singular decompositions of a cap-product
Résumé
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 the
intersection homology groups. In this work, we show that this classical cap-product is compatible
with 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 is
equivalent to the existence of an isomorphism between the intersection homology groups corresponding
to the zero and the top perversities. Our results answer a question asked by G. Friedman.
Domaines
Topologie algébrique [math.AT]
Origine : Fichiers produits par l'(les) auteur(s)
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