Poincaré duality with cap products in intersection homology

Abstract

For having a Poincaré duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an additional hypothesis on the torsion. In this work, by using the classical geometric process of blowing-up, adapted to a simplicial setting, we build a cochain complex which gives a Poincaré duality via a cap product with intersection homology, for any commutative ring of coefficients. We prove also the topological invariance of the blown-up intersection cohomology with compact supports in the case of a paracompact pseudomanifold with no codimension one strata. This work is written with general perversities, defined on each stratum and not only in function of the codimension of strata. It contains also a tame intersection homology, suitable for large perversities.

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References in corpus (1)

• Blown-up intersection cohomology

Cited by in corpus (6)

• Blown-up intersection cochains and Deligne's sheaves
• Poincaré duality, cap product and Borel-Moore intersection Homology
• Intersection Homology. General perversities and topological invariance
• A reasonable notion of dimension for singular intersection homology
• Simplicial intersection homology revisited
• Lefschetz duality for intersection (co)homology