Cup and cap products in intersection (co)homology

TL;DR

This paper develops cup and cap products within intersection (co)homology using field coefficients, providing a new proof of Poincare duality that parallels classical manifold theory.

Contribution

It introduces the construction of cup and cap products in intersection (co)homology, enabling a novel proof of Poincare duality similar to the classical case.

Findings

Constructed cup and cap products in intersection (co)homology.

Provided a new proof of Poincare duality in intersection (co)homology.

Extended classical duality concepts to singular spaces.

Abstract

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.