| Title:
|
Universal spaces for manifolds equipped with an integral closed $k$-form (English) |
| Author:
|
Lê, Hông-Vân |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
2007 |
| Pages:
|
443-457 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $U^{d(m,k)}$. (English) |
| Keyword:
|
closed $k$-form |
| Keyword:
|
universal space |
| Keyword:
|
$H$-principle |
| MSC:
|
53C10 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 1199.53077 |
| idMR:
|
MR2381787 |
| . |
| Date available:
|
2008-06-06T22:52:08Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108083 |
| . |
| Reference:
|
[1] Dold A., Thom R.: Quasifaserungen und unendliche symmetrische Produkte.Ann. of Math. 67 (2), (1958), 239–281. Zbl 0091.37102, MR 0097062 |
| Reference:
|
[2] Dold A., Puppe D.: Homologie nicht-additiver Funktoren. Anwendungen.Ann. Inst. Fourier (Grenoble) 11 (1961), 201–312. Zbl 0098.36005, MR 0150183 |
| Reference:
|
[3] Gromov M.: Partial Differential Relations.Springer-Verlag 1986, also translated in Russian, (1990), Moscow-Mir. Zbl 0651.53001, MR 0864505 |
| Reference:
|
[4] Gromov M.: .privat communication. Zbl 1223.37080 |
| Reference:
|
[5] Nash J.: The embedding problem for Riemannian manifolds.Ann. of Math. 63 (1), (1956), 20–63. MR 0075639 |
| Reference:
|
[6] Le H. V., Panák M., Vanžura J.: Manifolds admitting stable forms.Comment. Math. Univ. Carolin. (2007), to appear. Zbl 1212.53051, MR 2433628 |
| Reference:
|
[7] Thom R.: Quelques propriétés globales des variétés différentiables.Comment. Math. Helv. 28 (1954), 17–86. Zbl 0057.15502, MR 0061823 |
| Reference:
|
[8] Tischler D.: Closed 2-forms and an embedding theorem for symplectic manifolds.J. Differential Geom. 12 (1977), 229–235. Zbl 0386.58001, MR 0488108 |
| . |
