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

Archivum Mathematicum (2007)

- Volume: 043, Issue: 5, page 443-457
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topHông-Vân Lê. "Universal spaces for manifolds equipped with an integral closed $k$-form." Archivum Mathematicum 043.5 (2007): 443-457. <http://eudml.org/doc/250182>.

@article{Hông2007,

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 $U^\{d(m,k)\}$.},

author = {Hông-Vân Lê},

journal = {Archivum Mathematicum},

keywords = {closed $k$-form; universal space; $H$-principle; closed -form; universal space; -principle},

language = {eng},

number = {5},

pages = {443-457},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Universal spaces for manifolds equipped with an integral closed $k$-form},

url = {http://eudml.org/doc/250182},

volume = {043},

year = {2007},

}

TY - JOUR

AU - Hông-Vân Lê

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

JO - Archivum Mathematicum

PY - 2007

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 043

IS - 5

SP - 443

EP - 457

AB - 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 $U^{d(m,k)}$.

LA - eng

KW - closed $k$-form; universal space; $H$-principle; closed -form; universal space; -principle

UR - http://eudml.org/doc/250182

ER -

## References

top- Dold A., Thom R., Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (2), (1958), 239–281. (1958) Zbl0091.37102MR0097062
- Dold A., Puppe D., Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier (Grenoble) 11 (1961), 201–312. (1961) Zbl0098.36005MR0150183
- Gromov M., Partial Differential Relations, Springer-Verlag 1986, also translated in Russian, (1990), Moscow-Mir. (1986) Zbl0651.53001MR0864505
- Gromov M., [unknown], privat communication. Zbl1223.37080
- Nash J., The embedding problem for Riemannian manifolds, Ann. of Math. 63 (1), (1956), 20–63. (1956) MR0075639
- Le H. V., Panák M., Vanžura J., Manifolds admitting stable forms, Comment. Math. Univ. Carolin. (2007), to appear. Zbl1212.53051MR2433628
- Thom R., Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86. (1954) Zbl0057.15502MR0061823
- Tischler D., Closed 2-forms and an embedding theorem for symplectic manifolds, J. Differential Geom. 12 (1977), 229–235. (1977) Zbl0386.58001MR0488108

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.