Intersection numbers for normal functions

TL;DR

This paper introduces the concept of topological normal functions for primitive integral cohomology classes on complex projective manifolds and proves that their intersection numbers match those of the associated cohomology classes.

Contribution

It extends the notion of normal functions to a topological setting and establishes the equivalence of intersection numbers with classical cohomological intersection numbers.

Findings

Defined topological normal functions for primitive integral cohomology classes.

Proved the intersection number of topological normal functions equals that of their cohomology classes.

Provided a simplified proof of the intersection number equivalence.

Abstract

We expand the notion of a normal function for a Hodge class on an even-dimensional complex projective manifold to the notion of a 'topological normal function' associated to any primitive integral cohomology class. The definition of the intersection number of two topological normal functions is the analogue of that given by Griffiths and Green for classical normal functions. We give a simple proof that the intersection number of the normal functions is the same as the intersection number of their corresponding cohomology classes.