Explicit construction of Verdier-dual objects for intersection pairings

Develop an explicit construction of dual objects realizing Verdier duality for general reasonable topological spaces so that intersection pairings can be computed concretely, beyond the special case of locally compact oriented manifolds. The goal is to produce a concrete, practically usable realization of the Verdier-dual complexes that enables explicit intersection-number computations in the settings relevant to physics.

Background

In the paper, intersection pairings are framed in terms of dual vector spaces whose existence is guaranteed abstractly by Verdier duality. While the theory ensures the presence of appropriate dual complexes, in general these are described only up to universal properties and lack explicit, constructive realizations for broad classes of spaces.

The authors emphasize that an explicit and practical construction is needed to make intersection theory operational in physical applications, particularly for spaces that are not locally compact oriented manifolds.