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

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Hong-Van Le
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** 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.