Displaying similar documents to “A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds”

Holomorphic Poisson Cohomology

Zhuo Chen, Daniele Grandini, Yat-Sun Poon (2015)

Complex Manifolds

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Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients...

Nonclassical descriptions of analytic cohomology

Bailey, Toby N., Eastwood, Michael G., Gindikin, Simon G.

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Summary: There are two classical languages for analytic cohomology: Dolbeault and Čech. In some applications, however (for example, in describing the Penrose transform and certain representations), it is convenient to use some nontraditional languages. In [, and , J. Geom. Phys. 17, 231-244 (1995; Zbl 0861.22009)] was developed a language that allows one to render analytic cohomology in a purely holomorphic fashion.In this article we indicate a more general construction, which includes...

Logarithmic Poisson cohomology: example of calculation and application to prequantization

Joseph Dongho (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure. We prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kähler differentials. Therefore it induces a differential complex from which we derive the notion of logarithmic Poisson cohomology. We prove that Poisson cohomology and logarithmic Poisson cohomology are equal when the Poisson structure is log symplectic. We give an...

Remarks on the Lichnerowicz-Poisson cohomology

Izu Vaisman (1990)

Annales de l'institut Fourier

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The paper begins with some general remarks which include the Mayer-Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochshild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic,...

Hochschild cohomology and quantization of Poisson structures

Grabowski, Janusz

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It is well-known that the question of existence of a star product on a Poisson manifold N is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures P of the following type P = X Y with [ X , Y ] = u X + v Y , for some u , v C ( N , ) .