Geodesic
Differential complex associated to closed differential forms of nonconstant rank
Lobachevskii journal of mathematics, Tome 23 (2006), pp. 183-192
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present paper we construct a complex of sheaves associated to a closed differential form $\omega$. We study this complex in case $\omega$ is a) a closed 1-form vanishing at an embedded submanifold, b) a symplectic structure with Martinet singularities. In particular, we prove that, under additional conditions on $\omega$, this complex gives a fine resolution for the sheaf of infinitesimal automorphisms of $\omega$.
Keywords: complex of sheaves, closed 1-form, Martinet singularity, sheaf of infinitesimal automorphisms. 
@article{LJM_2006_23_a6,
     author = {M. A. Malakhaltsev},
     title = {Differential complex associated to closed differential forms of nonconstant rank},
     journal = {Lobachevskii journal of mathematics},
     pages = {183--192},
     year = {2006},
     volume = {23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_23_a6/}
}
TY  - JOUR
AU  - M. A. Malakhaltsev
TI  - Differential complex associated to closed differential forms of nonconstant rank
JO  - Lobachevskii journal of mathematics
PY  - 2006
SP  - 183
EP  - 192
VL  - 23
UR  - http://geodesic.mathdoc.fr/item/LJM_2006_23_a6/
LA  - en
ID  - LJM_2006_23_a6
ER  - 
%0 Journal Article
%A M. A. Malakhaltsev
%T Differential complex associated to closed differential forms of nonconstant rank
%J Lobachevskii journal of mathematics
%D 2006
%P 183-192
%V 23
%U http://geodesic.mathdoc.fr/item/LJM_2006_23_a6/
%G en
%F LJM_2006_23_a6
M. A. Malakhaltsev. Differential complex associated to closed differential forms of nonconstant rank. Lobachevskii journal of mathematics, Tome 23 (2006), pp. 183-192. http://geodesic.mathdoc.fr/item/LJM_2006_23_a6/

[1] Martinet J., “Sur les singularités des formes différetielles”, Ann. Inst. Fourier. Grenoble, 20:1 (1970), 95–178 | MR | Zbl

[2] M. Zhitomirskii, Singularities of foliations and vector fields, Lecture notes based on a course given ICTP-Trieste, 2003

[3] Cannas da Silva A., Guillemin V., Woodwart C., “On the unfolding of folded symplectic structures”, Math. Res. Lett., 7:1 (2000), 35–53 | MR | Zbl

[4] Cannas da Silva A., Fold-forms for four-folds, Preprint, 2003, 16 pp.

[5] Domitrz W., “Non-local invariants of Martinet's singular symplectic structure”, Banach Center Publ., 60 (2002), 122–143

[6] Molino P., Riemannian foliations, Birkhäuser, 1988 | MR | Zbl

[7] Vaisman I., Cohomology and Differential Forms, Marcel Dekker inc., New York, 1973 | MR | Zbl

[8] Bredon G. E., Sheaf theory, McGraw-Hill, New York, 1967 | MR | Zbl

[9] Russian Math. (Iz. VUZ), 47:11 (2003), 38–46 | MR

[10] Russian Math. (Iz. VUZ), 48:11 (2004), 41–47 | MR

[11] Pommaret J. F., Systems of partial differential equations and Lie pseudogroups, Math. Appl., 14, Gordon and Breach Science Publishers, New York | MR | Zbl

[12] Malakhaltsev M. A., “The Lie derivative and cohomology of $G$-structures”, Lobachevskii Journal of Mathematics, 3 (1999), 197–200 | MR | Zbl

[13] Postnikov M. M., Introduction to Morse theory, Nauka, 1971 | MR