Étude des Γ-structures de codimension 1 sur la sphère S 2
Roger, Claude
Annales de l'Institut Fourier, Tome 23 (1973), p. 213-227 / Harvested from Numdam
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Cet article contient une démonstration géométrique simple de π 2 (BΓ 1 r )=0 pour r=0,∞.

Ce résultat (démontré aussi par Mather comme corollaire d’un théorème beaucoup plus général) apparaît comme une conséquence du théorème de Michael Herman : Diff S 1 [ Diff S 1 , Diff S 1 ]=0.

L’appendice contient une étude des Γ structures sur les surfaces et un résultat sur la cohomologie de Diff S 1 .

This article contains a simple geometric demonstration of π 2 (BΓ 1 r )=0 for r=0,∞.

This result (which was also proved by Mather as a corollary of a far more general theorem) uses Michael Herman’s theorem: Diff S 1 [ Diff S 1 , Diff S 1 ]=0.

The reader will find in the appendix a study of Γ-structures on surfaces and a result about the cohomology group of Diff S 1 .

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     author = {Roger, Claude},
     title = {\'Etude des $\Gamma $-structures de codimension 1 sur la sph\`ere $S^2$},
     journal = {Annales de l'Institut Fourier},
     volume = {23},
     year = {1973},
     pages = {213-227},
     doi = {10.5802/aif.488},
     mrnumber = {50 \#1262},
     zbl = {0269.58006},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1973__23_4_213_0}
}

Roger, Claude. Étude des $\Gamma $-structures de codimension 1 sur la sphère $S^2$. Annales de l'Institut Fourier, Tome 23 (1973) pp. 213-227. doi : 10.5802/aif.488. http://gdmltest.u-ga.fr/item/AIF_1973__23_4_213_0/

[1] Haefliger, Feuilletage sur les variétés ouvertes, Topology 9 (1970). | MR 41 #7709 | Zbl 0196.26901

[2] Haefliger, Homotopy and Integrability, Manifolds Amsterdam, 1970, Springer 197. | Zbl 0215.52403

[3] Herman, C.R.A.S., 1971.

[4] Mather, On Haefliger's Classifying Space I, Bulletin AMS, 1971. | MR 44 #1047 | Zbl 0224.55022

[5] Mather, The Vanishing of the Homology of Certain Groups of Homomorphisms.

[6] Moser, A Rapidly Convergent Iteraction Method and non Linear Differential Equations II, Annali della Scuola Normale Superiore de Pisa, Vol. XX, pp. 499-535 (1966). | Numdam | MR 34 #6280 | Zbl 0174.47801

[7] Rosenberg et Thurston, Some Remarks on Foliations [Preprint]. | Zbl 0286.57014