About the foliations of fibered manifolds

Hamidou Dathe[1]; Cédric Tarquini[2]

  • [1] Département de Mathématiques et Informatique Faculté des Sciences et Techniques Université Cheikh Anta Diop Dakar Sénégal
  • [2] Lycée Chrestien de Troyes FRANCE

Annales mathématiques Blaise Pascal (2008)

  • Volume: 15, Issue: 2, page 211-232
  • ISSN: 1259-1734

Abstract

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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.

How to cite

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Dathe, Hamidou, and Tarquini, Cédric. "Sur les feuilletages des variétés fibrées." Annales mathématiques Blaise Pascal 15.2 (2008): 211-232. <http://eudml.org/doc/10561>.

@article{Dathe2008,
abstract = {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.},
affiliation = {Département de Mathématiques et Informatique Faculté des Sciences et Techniques Université Cheikh Anta Diop Dakar Sénégal; Lycée Chrestien de Troyes FRANCE},
author = {Dathe, Hamidou, Tarquini, Cédric},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Feuilletage; hyperbolique; lamination; ; fibered manifolds; exotic foliations; rigidity theorems},
language = {fre},
month = {7},
number = {2},
pages = {211-232},
publisher = {Annales mathématiques Blaise Pascal},
title = {Sur les feuilletages des variétés fibrées},
url = {http://eudml.org/doc/10561},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Dathe, Hamidou
AU - Tarquini, Cédric
TI - Sur les feuilletages des variétés fibrées
JO - Annales mathématiques Blaise Pascal
DA - 2008/7//
PB - Annales mathématiques Blaise Pascal
VL - 15
IS - 2
SP - 211
EP - 232
AB - 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.
LA - fre
KW - Feuilletage; hyperbolique; lamination; ; fibered manifolds; exotic foliations; rigidity theorems
UR - http://eudml.org/doc/10561
ER -

References

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  2. Christopher Ennis, Morris W. Hirsch, Charles Pugh, Foliations that are not approximable by smoother ones, Geometric dynamics (Rio de Janeiro, 1981) 1007 (1983), 146-176, Springer, Berlin Zbl0526.57018MR730269
  3. A. Fatihi, F. Laudenbach, V. Poenaru, Travaux de Thurston sur les surfaces, (1979), S.M.F, France 
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  7. Hiromichi Nakayama, Transversely affine foliations of some surface bundles over S 1 of pseudo-Anosov type, Ann. Inst. Fourier (Grenoble) 41 (1991), 755-778 Zbl0731.58053MR1136602
  8. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc 73 (1967), 747-817 Zbl0202.55202MR228014
  9. W. Thurston, Norm on the homology of 3 -manifolds, Memoirs of the A.M.S 339 (1986), 99-130 Zbl0585.57006MR823443
  10. W. Thurston, Three-dimensional geometry and topology, (1997), Princeton university press Zbl0873.57001MR1435975
  11. R. F. Williams, The DA-maps of smale and structural stability, Global analysis, Proc. Sym. Pure and Appl. Math 15 (1970), 329-334 Zbl0213.50303MR264705

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