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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Shadow forms of Brasselet-Goresky-MacPherson

Author: Belkacem Bendiffalah
Journal: Trans. Amer. Math. Soc. 347 (1995), 4747-4763
MSC: Primary 55N33; Secondary 14F32
MathSciNet review: 1316844
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Abstract: Brasselet, Goresky and MacPherson constructed an explicit morphism, providing a De Rham isomorphism between the intersection homology of a singular variety $ X$ and the cohomology of some complex of differential forms, called "shadow forms" and generalizing Whitney forms, on the smooth part of $ X$. The coefficients of shadow forms are integrals of Dirichlet type. We find an explicit formula for them; from that follows an alternative proof of Brasselet, Goresky and MacPherson's theorem. Next, we give a duality formula and a product formula for shadow forms and construct the correct algebra structure, for which shadow forms yield a morphism.

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Article copyright: © Copyright 1995 American Mathematical Society

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