Sur les feuilletages des variétés fibrées
Dathe, Hamidou ; Tarquini, Cédric
Annales mathématiques Blaise Pascal, Tome 15 (2008), p. 211-232 / Harvested from Numdam

Nous construisons un feuilletage exotique de classe C 1 sur tout fibré hyperbolique de genre 1. Nous montrons égalemnt des théorèmes de rigidité des feuilletages modèles sur certains fibrés pseudo-Anosov.

We build an example of C 1 -foliation which are not conjuguated to a model foliation on a hyperbolic three manifold. We also prove some rigidity theorems of modele foliations on pseudo-Anosov fibered manifolds. class file.

Publié le : 2008-01-01
DOI : https://doi.org/10.5802/ambp.248
Classification:  00X99
Mots clés: Feuilletage, hyperbolique, lamination,
@article{AMBP_2008__15_2_211_0,
     author = {Dathe, Hamidou and Tarquini, C\'edric},
     title = {Sur les feuilletages des vari\'et\'es fibr\'ees},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     year = {2008},
     pages = {211-232},
     doi = {10.5802/ambp.248},
     zbl = {1176.53036},
     mrnumber = {2473818},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AMBP_2008__15_2_211_0}
}
Dathe, Hamidou; Tarquini, Cédric. Sur les feuilletages des variétés fibrées. Annales mathématiques Blaise Pascal, Tome 15 (2008) pp. 211-232. doi : 10.5802/ambp.248. http://gdmltest.u-ga.fr/item/AMBP_2008__15_2_211_0/

[1] Denjoy, Arnaud Les trajectoires à la surface du tore., C. R. Acad. Sci., Paris, Tome 223 (1946), pp. 5-8 | MR 16554 | Zbl 0063.01085

[2] Ennis, Christopher; Hirsch, Morris W.; Pugh, Charles Foliations that are not approximable by smoother ones, Geometric dynamics (Rio de Janeiro, 1981), Springer, Berlin (Lecture Notes in Math.) Tome 1007 (1983), pp. 146-176 | MR 730269 | Zbl 0526.57018

[3] Fatihi, A.; Laudenbach, F.; Poenaru, V. Travaux de Thurston sur les surfaces, S.M.F, France (1979)

[4] Ghys, E.; Sergiescu, V. Stabilité et conjugaison différentiable pour certai ns feuilletages, Topology, Tome 19 (1980), pp. 179-197 | Article | MR 572582 | Zbl 0478.57017

[5] Hasselblatt, B.; Katok, A. Intoduction to the modern theory of dynamical systems, Cambridge University Press, Cambridge (1995) | MR 1326374 | Zbl 0878.58020

[6] Laudenbach, F.; Blank, S. Sur l’isotopie des formes fermées en dimension 3, Ivent. Math, Tome 54 (1979), pp. 103-177 | Article | Zbl 0435.58002

[7] Nakayama, Hiromichi Transversely affine foliations of some surface bundles over S 1 of pseudo-Anosov type, Ann. Inst. Fourier (Grenoble), Tome 41 (1991) no. 3, pp. 755-778 | Article | Numdam | MR 1136602 | Zbl 0731.58053

[8] Smale, S. Differentiable dynamical systems, Bull. Amer. Math. Soc, Tome 73 (1967), pp. 747-817 | Article | MR 228014 | Zbl 0202.55202

[9] Thurston, W. Norm on the homology of 3-manifolds, Memoirs of the A.M.S, Tome 339 (1986), pp. 99-130 | MR 823443 | Zbl 0585.57006

[10] Thurston, W. Three-dimensional geometry and topology, Princeton university press (1997) | MR 1435975 | Zbl 0873.57001

[11] Williams, R. F. The DA-maps of smale and structural stability, Global analysis, Proc. Sym. Pure and Appl. Math, Tome 15 (1970), pp. 329-334 | MR 264705 | Zbl 0213.50303