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 $U^{d(m,k)}$.
@article{108083,
author = {H\^ong-V\^an L\^e},
title = {Universal spaces for manifolds equipped with an integral closed $k$-form},
journal = {Archivum Mathematicum},
volume = {043},
year = {2007},
pages = {443-457},
zbl = {1199.53077},
mrnumber = {2381787},
language = {en},
url = {http://dml.mathdoc.fr/item/108083}
}
Hông-Vân Lê. Universal spaces for manifolds equipped with an integral closed $k$-form. Archivum Mathematicum, Tome 043 (2007) pp. 443-457. http://gdmltest.u-ga.fr/item/108083/
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