Geodesic
Universal spaces for manifolds equipped with an integral closed $k$-form
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 443-457 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $U^{d(m,k)}$.
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 
@article{ARM_2007_43_5_a8,
     author = {L\^e, H\^ong-V\^an},
     title = {Universal spaces for manifolds equipped with an integral closed $k$-form},
     journal = {Archivum mathematicum},
     pages = {443--457},
     year = {2007},
     volume = {43},
     number = {5},
     mrnumber = {2381787},
     zbl = {1199.53077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a8/}
}
TY  - JOUR
AU  - Lê, Hông-Vân
TI  - Universal spaces for manifolds equipped with an integral closed $k$-form
JO  - Archivum mathematicum
PY  - 2007
SP  - 443
EP  - 457
VL  - 43
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a8/
LA  - en
ID  - ARM_2007_43_5_a8
ER  - 
%0 Journal Article
%A Lê, Hông-Vân
%T Universal spaces for manifolds equipped with an integral closed $k$-form
%J Archivum mathematicum
%D 2007
%P 443-457
%V 43
%N 5
%U http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a8/
%G en
%F ARM_2007_43_5_a8
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/

[1] Dold A., Thom R.: Quasifaserungen und unendliche symmetrische Produkte. Ann. of Math. 67 (2), (1958), 239–281. | MR | Zbl

[2] Dold A., Puppe D.: Homologie nicht-additiver Funktoren. Anwendungen. Ann. Inst. Fourier (Grenoble) 11 (1961), 201–312. | MR | Zbl

[3] Gromov M.: Partial Differential Relations. Springer-Verlag 1986, also translated in Russian, (1990), Moscow-Mir. | MR | Zbl

[4] Gromov M.: privat communication. | Zbl

[5] Nash J.: The embedding problem for Riemannian manifolds. Ann. of Math. 63 (1), (1956), 20–63. | MR

[6] Le H. V., Panák M., Vanžura J.: Manifolds admitting stable forms. Comment. Math. Univ. Carolin. (2007), to appear. | MR | Zbl

[7] Thom R.: Quelques propriétés globales des variétés différentiables. Comment. Math. Helv. 28 (1954), 17–86. | MR | Zbl

[8] Tischler D.: Closed 2-forms and an embedding theorem for symplectic manifolds. J. Differential Geom. 12 (1977), 229–235. | MR | Zbl