Geodesic
Differential complex associated to closed differential forms of nonconstant rank
Lobachevskii journal of mathematics, Tome 23 (2006), pp. 183-192

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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},
     publisher = {mathdoc},
     volume = {23},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_23_a6/}
}
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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/