Poincar\'e duality, cap product and Borel-Moore intersection Homology

TL;DR

This paper constructs an explicit Poincaré duality isomorphism linking intersection cohomology and Borel-Moore intersection homology using cap products, applicable to a broad class of pseudomanifolds with coefficients in any commutative ring.

Contribution

It introduces a new explicit construction of Poincaré duality via cap products for intersection (co)homology on oriented pseudomanifolds.

Findings

Established a Poincaré duality isomorphism using cap products.

Applicable to any commutative ring of coefficients.

Works for second-countable, oriented pseudomanifolds.

Abstract

Using a cap product, we construct an explicit Poincar\'e duality isomorphism between the blown-up intersection cohomology and the Borel-Moore intersection homology, for any commutative ring of coefficients and second-countable, oriented pseudomanifolds.