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Logarithmic Poisson cohomology: example of calculation and application to prequantization

Joseph Dongho — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

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 example of...

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