Characteristic homomorphism for ( F 1 , F 2 ) -foliated bundles over subfoliated manifolds

José Manuel Carballés

Annales de l'institut Fourier (1984)

  • Volume: 34, Issue: 3, page 219-245
  • ISSN: 0373-0956

Abstract

top
In this paper a construction of characteristic classes for a subfoliation ( F 1 , F 2 ) is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of ( F 1 , F 2 ) -foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of F i -foliated bundles, i = 1 , 2 , the results of Kamber-Tondeur on the cohomology of g - D G -algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation are generalized, and the holonomy homomorphism of a leaf of a subfoliation is defined.

How to cite

top

Carballés, José Manuel. "Characteristic homomorphism for $(F_1,F_2)$-foliated bundles over subfoliated manifolds." Annales de l'institut Fourier 34.3 (1984): 219-245. <http://eudml.org/doc/74645>.

@article{Carballés1984,
abstract = {In this paper a construction of characteristic classes for a subfoliation $(F_1,F_2)$ is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of $(F_1,F_2)$-foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of $F_i$-foliated bundles, $i=1,2$, the results of Kamber-Tondeur on the cohomology of $g$-$DG$-algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation are generalized, and the holonomy homomorphism of a leaf of a subfoliation is defined.},
author = {Carballés, José Manuel},
journal = {Annales de l'institut Fourier},
keywords = {characteristic classes for a subfoliation; characteristic homomorphism; algebra of characteristic invariants; cohomology of g-DG-algebras; restriction of foliated bundles to the leaves; holonomy homomorphism of a leaf of a subfoliation; subfoliated bundles},
language = {eng},
number = {3},
pages = {219-245},
publisher = {Association des Annales de l'Institut Fourier},
title = {Characteristic homomorphism for $(F_1,F_2)$-foliated bundles over subfoliated manifolds},
url = {http://eudml.org/doc/74645},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Carballés, José Manuel
TI - Characteristic homomorphism for $(F_1,F_2)$-foliated bundles over subfoliated manifolds
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 3
SP - 219
EP - 245
AB - In this paper a construction of characteristic classes for a subfoliation $(F_1,F_2)$ is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of $(F_1,F_2)$-foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of $F_i$-foliated bundles, $i=1,2$, the results of Kamber-Tondeur on the cohomology of $g$-$DG$-algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation are generalized, and the holonomy homomorphism of a leaf of a subfoliation is defined.
LA - eng
KW - characteristic classes for a subfoliation; characteristic homomorphism; algebra of characteristic invariants; cohomology of g-DG-algebras; restriction of foliated bundles to the leaves; holonomy homomorphism of a leaf of a subfoliation; subfoliated bundles
UR - http://eudml.org/doc/74645
ER -

References

top
  1. [1] G. ANDRZEJCZAK, Some characteristic invariants of foliated bundles, Institute of Mathematics, Polish Academy of Sciences, Preprint 182, Warszawa, 1979. Zbl0538.57013
  2. [2] R. BOTT, Lectures on characteristic classes and foliations, Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972. Zbl0241.57010MR50 #14777
  3. [3] L.A. CORDERO and P.M. GADEA, Exotic characteristic classes and subfoliations, Ann. Inst. Fourier, Grenoble, 26-1 (1976), 225-237 ; errata, ibid. 27, fasc. 4 (1977). Zbl0313.57010MR53 #6584
  4. [4] L.A. CORDERO and X. MASA, Characteristic classes of subfoliations, Ann. Inst. Fourier, Grenoble, 31-2 (1981), 61-86. Zbl0442.57009MR83a:57033
  5. [5] B.L. FEIGIN, Characteristic classes of flags of foliations, Funct. Anal. and its Appl., 9 (1975), 312-317. Zbl0328.57008MR53 #6585
  6. [6] R. GOLDMAN, The holonomy ring of the leaves of foliated manifolds, J. Differential Geometry, 11 (1976), 411-449. Zbl0356.57016MR56 #3852
  7. [7] F.W. KAMBER and Ph. TONDEUR, Foliated bundles and characteristic classes, Lecture Notes in Math., Vol 493, Springer, Berlin, 1975. Zbl0308.57011MR53 #6587
  8. [8] X. MASA, Characteristic classes of subfoliations II, preprint. 
  9. [9] R. MOUSSU, Sur les classes exotiques des feuilletages, Lecture Notes in Math., Vol. 392, Springer, Berlin, 1974, 37-42. Zbl0292.57021MR50 #14785
  10. [10] B.L. REINHART, Holonomy invariants for framed foliations, Lecture Notes in Math., Vol. 392, Springer, Berlin, 1974, 47-52. Zbl0291.57017MR51 #1842

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.