On the Cech bicomplex associated with foliated structures

Haruo Kitahara; Shinsuke Yorozu

Annales de l'institut Fourier (1978)

  • Volume: 28, Issue: 3, page 217-224
  • ISSN: 0373-0956

Abstract

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

How to cite

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Kitahara, Haruo, and Yorozu, Shinsuke. "On the Cech bicomplex associated with foliated structures." Annales de l'institut Fourier 28.3 (1978): 217-224. <http://eudml.org/doc/74373>.

@article{Kitahara1978,
abstract = {For a codimension $q$ foliation on a manifold, $\eta \times (d\eta )^q$ defines the Godbillon-Vey class. We show that $\eta $ itself defines a certain cohomology class, via the Cech bicomplex.},
author = {Kitahara, Haruo, Yorozu, Shinsuke},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {217-224},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the Cech bicomplex associated with foliated structures},
url = {http://eudml.org/doc/74373},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Kitahara, Haruo
AU - Yorozu, Shinsuke
TI - On the Cech bicomplex associated with foliated structures
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 3
SP - 217
EP - 224
AB - For a codimension $q$ foliation on a manifold, $\eta \times (d\eta )^q$ defines the Godbillon-Vey class. We show that $\eta $ itself defines a certain cohomology class, via the Cech bicomplex.
LA - eng
UR - http://eudml.org/doc/74373
ER -

References

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  1. [1] R. BOTT, Lectures on characteristic classes and foliations, Lecture Notes in Math., Springer, 279 (1972), 1-94. Zbl0241.57010MR50 #14777
  2. [2] C. GODBILLON and J. VEY, Un invariant des feuilletages de codimension 1, C.R. Acad. Sci., Paris, 273 (1971), A92-95. Zbl0215.24604MR44 #1046
  3. [3] F.W. KAMBER and P. TONDEUR, Foliated bundles and characteristic classes, Lecture Notes in Math., Springer, 493 (1975). Zbl0308.57011MR53 #6587
  4. [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. Zbl0318.57028MR53 #11628
  5. [5] G. REEB, Sur certaines propriétés topologiques des variétés feuilletées, Hermann (1952). Zbl0049.12602MR14,1113a
  6. [6] Y. SHIKATA, On the spectral sequences associated to foliated structures, Nagoya Math. J., 38 (1970), 53-61. Zbl0193.52602
  7. [7] Y. SHIKATA, On the cohomology of bigraded forms associated with foliated structures, Bull. Soc. Math. Grèce, 15 (1974), 68-76. Zbl0321.57016MR58 #31107
  8. [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. Zbl0301.57011MR52 #9246

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