On the Cech bicomplex associated with foliated structures
Annales de l'Institut Fourier, Volume 28 (1978) no. 3, pp. 217-224.

For a codimension q foliation on a manifold, η×(dη) q defines the Godbillon-Vey class. We show that η itself defines a certain cohomology class, via the Cech bicomplex.

Pour un feuilletage de codimension q sur une variété, η×(dη) q définit la classe de Godbillon-Vey. On démontre que η définit une certaine classe de cohomologie, via la bicomplexe de Cech.

@article{AIF_1978__28_3_217_0,
     author = {Kitahara, Haruo and Yorozu, Shinsuke},
     title = {On the {Cech} bicomplex associated with foliated structures},
     journal = {Annales de l'Institut Fourier},
     pages = {217--224},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {28},
     number = {3},
     year = {1978},
     doi = {10.5802/aif.711},
     zbl = {0368.57006},
     mrnumber = {80c:57016a},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.711/}
}
TY  - JOUR
TI  - On the Cech bicomplex associated with foliated structures
JO  - Annales de l'Institut Fourier
PY  - 1978
DA  - 1978///
SP  - 217
EP  - 224
VL  - 28
IS  - 3
PB  - Imprimerie Louis-Jean
PP  - Gap
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.711/
UR  - https://zbmath.org/?q=an%3A0368.57006
UR  - https://www.ams.org/mathscinet-getitem?mr=80c:57016a
UR  - https://doi.org/10.5802/aif.711
DO  - 10.5802/aif.711
LA  - en
ID  - AIF_1978__28_3_217_0
ER  - 
%0 Journal Article
%T On the Cech bicomplex associated with foliated structures
%J Annales de l'Institut Fourier
%D 1978
%P 217-224
%V 28
%N 3
%I Imprimerie Louis-Jean
%C Gap
%U https://doi.org/10.5802/aif.711
%R 10.5802/aif.711
%G en
%F AIF_1978__28_3_217_0
Kitahara, Haruo; Yorozu, Shinsuke. On the Cech bicomplex associated with foliated structures. Annales de l'Institut Fourier, Volume 28 (1978) no. 3, pp. 217-224. doi : 10.5802/aif.711. https://aif.centre-mersenne.org/articles/10.5802/aif.711/

[1] R. Bott, Lectures on characteristic classes and foliations, Lecture Notes in Math., Springer, 279 (1972), 1-94. | MR: 50 #14777 | Zbl: 0241.57010

[2] C. Godbillon and J. Vey, Un invariant des feuilletages de codimension 1, C.R. Acad. Sci., Paris, 273 (1971), A92-95. | MR: 44 #1046 | Zbl: 0215.24604

[3] F.W. Kamber and P. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Math., Springer, 493 (1975). | MR: 53 #6587 | Zbl: 0308.57011

[4] H. Kitahara and S. Yorozu, Sur l'homomorphisme de Chern-Weil local et ses applications au feuilletage, C.R. Acad. Sci., Paris, 281 (1975), A703-706. | MR: 53 #11628 | Zbl: 0318.57028

[5] G. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Hermann (1952). | MR: 14,1113a | Zbl: 0049.12602

[6] Y. Shikata, On the spectral sequences associated to foliated structures, Nagoya Math. J., 38 (1970), 53-61. | Zbl: 0193.52602

[7] Y. Shikata, On the cohomology of bigraded forms associated with foliated structures, Bull. Soc. Math. Grèce, 15 (1974), 68-76. | MR: 58 #31107 | Zbl: 0321.57016

[8] A. So, J.C. Thomas and C. Watkiss, Sur la multiplicativité de l'homomorphisme de Chern-Weil local, C.R. Acad. Sci., Paris, 280 (1975), A369-371. | MR: 52 #9246 | Zbl: 0301.57011

Cited by Sources: