Universal spaces for manifolds equipped with an integral closed $k$-form

Hong-Van Le

Address. Mathematical Institute of Academy of Science
Zitna 25, 115 67 Praha 1, Czech Republic

E-mail: hvle@math.cas.cz

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 $U^{d(m,k)}$.

AMSclassification. 53C10, 53C42.

Keywords. Closed $k$-form, universal space, $H$-principle.