Comptes Rendus
no. 3
Géométrie différentielle, Systèmes dynamiques
Deformation of singular foliations, 1: Local deformation cohomology
Philippe Monnier1 ; Tien Zung Nguyen1
1 Institut de Mathématiques de Toulouse, UMR 5219 CNRS, Université Toulouse III, France
Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 273-283.

In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study it in the local case, i.e., in the neighborhood of a point.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.26
Philippe Monnier 1 ; Tien Zung Nguyen 1

1 Institut de Mathématiques de Toulouse, UMR 5219 CNRS, Université Toulouse III, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2020__358_3_273_0,
     author = {Philippe Monnier and Tien Zung Nguyen},
     title = {Deformation of singular foliations, 1: {Local} deformation cohomology},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {273--283},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {3},
     year = {2020},
     doi = {10.5802/crmath.26},
     language = {en},
}
TY  - JOUR
AU  - Philippe Monnier
AU  - Tien Zung Nguyen
TI  - Deformation of singular foliations, 1: Local deformation cohomology
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 273
EP  - 283
VL  - 358
IS  - 3
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.26
LA  - en
ID  - CRMATH_2020__358_3_273_0
ER  - 
%0 Journal Article
%A Philippe Monnier
%A Tien Zung Nguyen
%T Deformation of singular foliations, 1: Local deformation cohomology
%J Comptes Rendus. Mathématique
%D 2020
%P 273-283
%V 358
%N 3
%I Académie des sciences, Paris
%R 10.5802/crmath.26
%G en
%F CRMATH_2020__358_3_273_0
Philippe Monnier; Tien Zung Nguyen. Deformation of singular foliations, 1: Local deformation cohomology. Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 273-283. doi : 10.5802/crmath.26. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.26/

[1] Iakovos Androulidakis; Georges Skandalis The holonomy groupoid of a singular foliation, J. Reine Angew. Math., Volume 626 (2009), pp. 1-37 | DOI | MR | Zbl

[2] Iakovos Androulidakis; Marco Zambon Stefan–Sussmann singular foliations, singular subalgebroids and their associated sheaves, Int. J. Geom. Methods Mod. Phys., Volume 13 (2016), 1641001, 17 pages | MR | Zbl

[3] Vladimir I. Arnold; Sabir M. Gusein-Zade; Alexander N. Varchenko Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts, Monographs in Mathematics, 82, Birkhäuser, 1985 | Zbl

[4] Jean-Paul Dufour; Nguyen Tien Zung Linearization of Nambu structures, Compos. Math., Volume 117 (1999) no. 1, p. 77--98 | MR | Zbl

[5] Jean-Paul Dufour; Nguyen Tien Zung Poisson structures and their normal forms, Progress in Mathematics, 242, Birkhäuser, 2005 | MR | Zbl

[6] James L. Heitsch A cohomology for foliated manifolds, Comment. Math. Helv., Volume 50 (1975), pp. 197-218 | DOI | MR | Zbl

[7] Robert Hermann On the accessibility problem in control theory, International symposium on nonlinear differential equations and nonlinear mechanics, Academic Press Inc., 1963, pp. 327-332 | Zbl

[8] Bernard Malgrange Frobenius avec singularités. II. Le cas général, Invent. Math., Volume 39 (1977) no. 1, pp. 67-89 | DOI | Zbl

[9] Truong Hong Minh; Nguyen Tien Zung Commuting Foliations, Regul. Chaotic Dyn., Volume 18 (2013) no. 6, pp. 608-622 | MR | Zbl

[10] Philippe Monnier Computations of Nambu-Poisson cohomologies, Int. J. Math., Volume 26 (2001) no. 2, pp. 65-81 | DOI | MR | Zbl

[11] Philippe Monnier Poisson cohomology in dimension two, Isr. J. Math., Volume 129 (2002), pp. 189-207 | DOI | MR | Zbl

[12] Georges Reeb Sur les espaces fibrés et les variétés feuilletées. II: Sur certaines propriétés topologiques des variétés feuilletées (Actualités scientifiques et industrielles), Volume 1183, Hermann & Cie, 1952, p. 5-89, 155–156 | Zbl

[13] Peter Stefan Accessible sets, orbits, and foliations with singularities, Proc. Lond. Math. Soc., Volume 29 (1974), pp. 699-713 | DOI | MR | Zbl

[14] Hector J. Sussmann Orbits of families of vector fields and integrability of distributions, Trans. Am. Math. Soc., Volume 180 (1973), pp. 171-188 | DOI | MR | Zbl

[15] William P. Thurston A generalization of the Reeb stability theorem, Topology, Volume 13 (1974), pp. 347-352 | DOI | MR | Zbl

[16] Nguyen Tien Zung New results on the linearization of Nambu structures, J. Math. Pures Appl., Volume 99 (2013) no. 2, pp. 211-218 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Classification of bm-Nambu structures of top degree

Eva Miranda; Arnau Planas

C. R. Math (2018)

Prehistory of the Higgs boson

Peter Higgs

C. R. Phys (2007)

Spontaneous broken symmetry

Robert Brout; François Englert

C. R. Phys (2007)