no. 3
Transversely affine foliations of some surface bundles over S 1 of pseudo-Anosov type
Annales de l'Institut Fourier, Tome 41 (1991) no. 3, pp. 755-778.

Nous considérons des feuilletages transversalement affines sans feuille compacte sur des fibrés en surfaces de genre plus grand que 1 au-dessus du cercle de type pseudo-Anosov tels que les classes d’Euler des fibrés tangents des feuilletages coïncident avec celle du feuilletage par fibres. Nous classifions de tels feuilletages sur les fibrés sont les monodromies satisfont une certaine condition.

We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.

@article{AIF_1991__41_3_755_0,
     author = {Nakayama, Hiromichi},
     title = {Transversely affine foliations of some surface bundles over $S^1$ of {pseudo-Anosov} type},
     journal = {Annales de l'Institut Fourier},
     pages = {755--778},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {41},
     number = {3},
     year = {1991},
     doi = {10.5802/aif.1272},
     mrnumber = {92k:57055},
     zbl = {0731.58053},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1272/}
}
TY  - JOUR
AU  - Nakayama, Hiromichi
TI  - Transversely affine foliations of some surface bundles over $S^1$ of pseudo-Anosov type
JO  - Annales de l'Institut Fourier
PY  - 1991
SP  - 755
EP  - 778
VL  - 41
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.1272/
DO  - 10.5802/aif.1272
LA  - en
ID  - AIF_1991__41_3_755_0
ER  - 
%0 Journal Article
%A Nakayama, Hiromichi
%T Transversely affine foliations of some surface bundles over $S^1$ of pseudo-Anosov type
%J Annales de l'Institut Fourier
%D 1991
%P 755-778
%V 41
%N 3
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.1272/
%R 10.5802/aif.1272
%G en
%F AIF_1991__41_3_755_0
Nakayama, Hiromichi. Transversely affine foliations of some surface bundles over $S^1$ of pseudo-Anosov type. Annales de l'Institut Fourier, Tome 41 (1991) no. 3, pp. 755-778. doi : 10.5802/aif.1272. http://archive.numdam.org/articles/10.5802/aif.1272/

[1] A. Fathi, F. Laudenbach and V. Poénaru, Travaux de Thurston sur les surfaces, Séminaire Orsay, Astérisque, vol. 66-67 (1979). | Numdam | MR | Zbl

[2] E. Ghys and V. Sergiescu, Stabilité et conjugaison différentiable pour certains feuilletages, Topology, 19 (1980), 179-197. | MR | Zbl

[3] G. Hector and U. Hirsch, Introduction to the geometry of foliations, Part B, Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden, 1983. | Zbl

[4] T. Inaba, Resilient leaves in transversely affine foliations, Tôhoku Math. J., (2) 41 (1989), 625-631. | MR | Zbl

[5] T. Inaba and S. Matsumoto, Non-singular expansive flows on 3-manifolds and foliations with round prong singularities, preprint, 1989.

[6] F. Laudenbach and S. Blank, Isotopie de formes fermées en dimension trois, Invent. Math., 54 (1979), 103-177. | MR | Zbl

[7] G. Levitt, Pantalons et feuilletages des surfaces, Topology, 21 (1982), 9-33. | MR | Zbl

[8] G. Meigniez, Actions de groupes sur la droite et feuilletages de codimension 1, Thèse, Université Claude Bernard-Lyon I, 1988.

[9] H. Nakayama, On cutting pseudo-foliations along incompressible surfaces, preprint, 1988. | Zbl

[10] S.P. Novikov, Topology of foliations, Trudy Moskov Mat. Obshch., 14 (1965), 248-278, Trans. Moscow Math. Soc., 14 (1965), 268-304. | MR | Zbl

[11] R. Roussarie, Plongements dans les variétés feuilletées et classification de feuilletages sans holonomie, Publ. Math. I.H.E.S., 43 (1974), 101-141. | Numdam | MR | Zbl

[12] B. Seke, Sur les structures transversalement affines des feuilletages de codimension un, Ann. Inst. Fourier (Grenoble), 30-4 (1980), 1-29. | Numdam | MR | Zbl

[13] V.V. Solodov, Components of topological foliations, Math. USSR-Sbornik, 47 (1984), 329-343. | Zbl

[14] I. Tamura and A. Sato, On transverse foliations, Publ. Math. I.H.E.S., 54 (1981), 5-35. | Numdam | MR | Zbl

[15] W. Thurston, A norm for the homology of 3-manifolds, Mem. A.M.S., 59, No. 339 (1986), 99-130. | MR | Zbl

[16] W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. A.M.S., 19 (1988), 417-431. | MR | Zbl

[17] N. Tsuchiya, Elementary transversely affine foliations, preprint, 1989.

Cité par Sources :