Geodesic
Universal spaces for manifolds equipped with an integral closed $k$-form
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 443-457.

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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 $U^{d(m,k)}$.
Classification : 53C10, 53C42
Keywords: closed $k$-form; universal space; $H$-principle 
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     title = {Universal spaces for manifolds equipped with an integral closed $k$-form},
     journal = {Archivum mathematicum},
     pages = {443--457},
     publisher = {mathdoc},
     volume = {43},
     number = {5},
     year = {2007},
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     zbl = {1199.53077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a8/}
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Lê, Hông-Vân. Universal spaces for manifolds equipped with an integral closed $k$-form. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 443-457. http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a8/