Singular decompositions of a cap-product

Abstract : 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.
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  • ARXIV : 1606.04233

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David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré. Singular decompositions of a cap-product. Proceedings of the AMS, 2017, 145 (8), pp.3645-3656. ⟨hal-01332473⟩

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