Foliations of M 3 defined by 2 -actions
Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 1091-1118.

In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of 2 .

Dans cet article on donne une caractérisation géométrique des feuilletages de dimension 2 sur les variétés compactes orientables de dimension 3, définis par une action différentiable localement libre de 2 .

@article{AIF_1995__45_4_1091_0,
     author = {Arraut, Jose Luis and Craizer, Marcos},
     title = {Foliations of $M^3$ defined by ${\mathbb {R}}^2$-actions},
     journal = {Annales de l'Institut Fourier},
     pages = {1091--1118},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {45},
     number = {4},
     year = {1995},
     doi = {10.5802/aif.1486},
     mrnumber = {96j:57030},
     zbl = {0833.57014},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1486/}
}
TY  - JOUR
AU  - Arraut, Jose Luis
AU  - Craizer, Marcos
TI  - Foliations of $M^3$ defined by ${\mathbb {R}}^2$-actions
JO  - Annales de l'Institut Fourier
PY  - 1995
SP  - 1091
EP  - 1118
VL  - 45
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.1486/
DO  - 10.5802/aif.1486
LA  - en
ID  - AIF_1995__45_4_1091_0
ER  - 
%0 Journal Article
%A Arraut, Jose Luis
%A Craizer, Marcos
%T Foliations of $M^3$ defined by ${\mathbb {R}}^2$-actions
%J Annales de l'Institut Fourier
%D 1995
%P 1091-1118
%V 45
%N 4
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.1486/
%R 10.5802/aif.1486
%G en
%F AIF_1995__45_4_1091_0
Arraut, Jose Luis; Craizer, Marcos. Foliations of $M^3$ defined by ${\mathbb {R}}^2$-actions. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 1091-1118. doi : 10.5802/aif.1486. http://archive.numdam.org/articles/10.5802/aif.1486/

[1]J.L. Arraut and M. Craizer, Stability of blocks of compact orbits of an action of ℝ2 on M3. Hamiltonian Systems and Celestial Mechanics., Edited by E.A. Lacomba and J. Libre, World Scientific (1993). | Zbl

[2]J.L. Arraut and N.M. Dos Santos, Differentiable conjugation of actions of Rp, Bol. Soc. Bras. Mat., vol. 19, n.1 (1988), 1-19. | MR | Zbl

[3]G. Chatelet and H. Rosenberg, Un théorème de conjugaison des feuilletages, Ann. Inst. Fourier, Grenoble, 21-3 (1971), 95-106. | Numdam | MR | Zbl

[4]G. Chatelet, H. Rosenberg and D. Weil, A classification of the topological types of ℝ2-actions on closed orientable 3-manifolds, Publ. Math. IHES, 43 (1973), 261-272. | Numdam | MR | Zbl

[5]E. Ghys, T. Tsuboi, Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1, Ann. Inst. Fourier, Grenoble, 38-1 (1988), 215-244. | Numdam | MR | Zbl

[6]N. Koppel, Commuting diffeomorphisms. Global Analysis, Proc. of Symp. in Pure Math., AMS, XIV (1970). | Zbl

[7]E.L. Lima, Commuting Vector Fields on S3, Annals of Math., 81 (1965), 70-81. | MR | Zbl

[8]R. Moussu, R. Roussarie, Relations de conjugaison et de cobordisme entre certains feuilletages, Pub. Math. IHES, 43 (1973), 143-168. | Numdam | MR | Zbl

[9]H. Rosenberg, R. Roussarie and D. Weil, A classification of closed orientable manifolds of rank two, Ann. of Math., 91 (1970), 449-464. | MR | Zbl

[10]H. Rosenberg and R. Roussarie, Topological equivalence of Reeb foliations, Topology, vol. 9 (1970), 231-242. | MR | Zbl

[11]N.C. Saldanha, Stability of compact actions of Rn of codimension one, to appear in Comm. Math. Helvet. | Zbl

[12]F. Sergeraert, Feuilletages et difféomorphismes infiniment tangents à l'identité, Inventiones Math., 39 (1977), 253-275. | MR | Zbl

[13]G. Szekeres, Regular iteration of real and complex functions, Acta Math., 100 (1958), 163-195. | MR | Zbl

[14]J.-C. Yoccoz, Thesis.

[15]M. Craizer, Homogenization of codimension 1 actions of near a compact orbit, ℝn Ann. Inst. Fourier, Grenoble, 44-5 (1994), 1435-1448. | Numdam | MR | Zbl

Cited by Sources: