Universal spaces for manifolds equipped with a closed integral k-form

TL;DR

This paper proves that any closed integral k-form on a manifold can be realized as a restriction of a universal closed k-form on a higher-dimensional universal manifold, via an embedding.

Contribution

It introduces the concept of universal spaces for manifolds with closed integral k-forms and constructs such universal forms explicitly.

Findings

Any integral closed k-form on a manifold is the restriction of a universal form.

Existence of a universal manifold embedding for manifolds with closed forms.

Universal forms provide a unifying framework for studying closed k-forms.

Abstract

In this note we prove that any integral closed k-form $\phi ^k$, $k\ge 3$, on a m-dimensional manifold $M^m$, $m \ge k$, is the restriction of a universal closed k-form $h^k$ on a universal manifold $U^{d(m,k)}$ as a result of an embedding of $M^m$ to $U^{d(m,k)}$.