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

Abstract

In this note we prove that any integral closed k-form $ϕ^k$, $k\ge 3$, 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 $U^{d(m,k)}$.