We prove that a closed 3-dimensional manifold is a torus bundle over the circle if and only if it carries a closed nonsingular 1-form which is linearly deformable into contact forms.
Consider a complex analytic manifold X and a coherent Lie subalgebra I of the Lie algebra of complex vector fields on X. By using a natural D X -module M I naturally associated to I and the ring (in the derived sense) RH om D X (M I , M I ), we associate integers which measure the irregularity of the foliation associated with I .
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