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Leibniz cohomology for differentiable manifolds

Jerry M. Lodder (1998)

Annales de l'institut Fourier

We propose a definition of Leibniz cohomology, H L * , for differentiable manifolds. Then H L * becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of H L * ( R n ; R ) reduce to those of formal vector fields, and can be identified with certain invariants of foliations.

Lemme de Moser feuilleté et clasifications des variétés de Poisson régulières.

G. Héctor, E. Macías, M. Saralegui (1989)

Publicacions Matemàtiques

Regular Poisson structures with fixed characteristic foliation F are described by means of foliated symplectic forms. Associated to each of these structures, there is a class in the second group of foliated cohomology H2(F). Using a foliated version of Moser's lemma, we study the isotopy classes of these structures in relation with their cohomology class. Explicit examples, with dim F = 2, are described.

L'espace des feuilletages d'un espace analytique compact

Daniel Barlet (1987)

Annales de l'institut Fourier

Nous construisons sur l’ensemble des feuilletages (avec singulariés) d’un espace analytique compact normal une structure analytique complexe. Dans le cas faiblement kählérien, nous montrons qu’à un point frontière de la compactification naturelle de l’espace des feuilletages est encore associé un feuilletage.

Lie algebras of vector fields and codimension one foliations.

Tomasz Rybicki (1990)

Publicacions Matemàtiques

The main result is a Pursell-Shanks type theorem for codimension one foliations. This theorem can be viewed as a partial solution of a hypothetical general version of the theorem of Pursell-Shanks. Several propositions and lemmas on foliations are contained in the proof.

Line bundles with c 1 L 2 = 0

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that on a C W -complex the obstruction for a line bundle L to be the fractional power of a suitable pullback of the Hopf bundle on a 2-dimensional sphere is the vanishing of the square of the first Chern class of L . On the other hand we show that if one looks at integral powers then further secondary obstructions exist.

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