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Area functionals and Godbillon-Vey cocycles

Takashi Tsuboi (1992)

Annales de l'institut Fourier

We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.


Francis Sergeraert (1977/1978)

Séminaire Bourbaki

Existence of star-products on exact symplectic manifolds

Marc De Wilde, P. B. A. Lecomte (1985)

Annales de l'institut Fourier

It is shown that if a manifold admits an exact symplectic form, then its Poisson Lie algebra has non trivial formal deformations and the manifold admits star-products. The non-formal derivations of the star-products and the deformations of the Poisson Lie algebra of an arbitrary symplectic manifold are studied.

Non-degenerescence of some spectral sequences

K. S. Sarkaria (1984)

Annales de l'institut Fourier

Each Lie algebra of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold M définies, in a natural way, a spectral sequence E k ( ) which converges to the de Rham cohomology of M in a finite number of steps. We prove e.g. that for all k 0 there exists a foliated compact manifold with E k ( ) infinite dimensional.

On the cohomology of vector fields on parallelizable manifolds

Yuly Billig, Karl-Hermann Neeb (2008)

Annales de l’institut Fourier

In the present paper we determine for each parallelizable smooth compact manifold M the second cohomology spaces of the Lie algebra 𝒱 M of smooth vector fields on M with values in the module Ω ¯ M p = Ω M p / d Ω M p - 1 . The case of p = 1 is of particular interest since the gauge algebra of functions on M with values in a finite-dimensional simple Lie algebra has the universal central extension with center Ω ¯ M 1 , generalizing affine Kac-Moody algebras. The second cohomology H 2 ( 𝒱 M , Ω ¯ M 1 ) classifies twists of the semidirect product of 𝒱 M with the...

On the first homology of automorphism groups of manifolds with geometric structures

Kōjun Abe, Kazuhiko Fukui (2005)

Open Mathematics

Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.

On the real secondary classes of transversely holomorphic foliations

Taro Asuke (2000)

Annales de l'institut Fourier

In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space H * ( WO 2 q ) of the real secondary classes to the space H * ( WU q ) of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also...

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