Sur les feuilletages des variétés fibrées
[About the foliations of fibered manifolds]
Annales Mathématiques Blaise Pascal, Volume 15 (2008) no. 2, pp. 211-232.

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.

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.

DOI: 10.5802/ambp.248
Classification: 00X99
Keywords: Feuilletage, hyperbolique, lamination,
@article{AMBP_2008__15_2_211_0,
     author = {Hamidou Dathe and C\'edric Tarquini},
     title = {Sur les feuilletages des vari\'et\'es fibr\'ees},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {211--232},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {2},
     year = {2008},
     doi = {10.5802/ambp.248},
     mrnumber = {2473818},
     zbl = {1176.53036},
     language = {fr},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.248/}
}
TY  - JOUR
TI  - Sur les feuilletages des variétés fibrées
JO  - Annales Mathématiques Blaise Pascal
PY  - 2008
DA  - 2008///
SP  - 211
EP  - 232
VL  - 15
IS  - 2
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.248/
UR  - https://www.ams.org/mathscinet-getitem?mr=2473818
UR  - https://zbmath.org/?q=an%3A1176.53036
UR  - https://doi.org/10.5802/ambp.248
DO  - 10.5802/ambp.248
LA  - fr
ID  - AMBP_2008__15_2_211_0
ER  - 
%0 Journal Article
%T Sur les feuilletages des variétés fibrées
%J Annales Mathématiques Blaise Pascal
%D 2008
%P 211-232
%V 15
%N 2
%I Annales mathématiques Blaise Pascal
%U https://doi.org/10.5802/ambp.248
%R 10.5802/ambp.248
%G fr
%F AMBP_2008__15_2_211_0
Hamidou Dathe; Cédric Tarquini. Sur les feuilletages des variétés fibrées. Annales Mathématiques Blaise Pascal, Volume 15 (2008) no. 2, pp. 211-232. doi : 10.5802/ambp.248. https://ambp.centre-mersenne.org/articles/10.5802/ambp.248/

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

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

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

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

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

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

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

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

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

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

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

Cited by Sources: