Differential complex associated to closed differential forms of nonconstant rank

M. A. Malakhaltsev

Kazan State University

Abstract: 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.

Submitted by: V. V. Lychagin
Received: 02.08.2006

Language: English

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