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Abstract: The unimodularity condition for a Poisson structure ie., a Poisson structurewith a trivial modular class induces a Poincar\-e duality between its Poissonhomology and its Poisson cohomology. Therefore an information about the Poissonhomology of this kind Poisson structures induces by duality an informationabout its Poisson cohomology and vise versa. But this is not longer true in thecase of a non trivial modular class. That is the case of Generalized JacobianPoisson Structures GJPS. In this paper, we consider certain GJPS in dimension3 and obtain properties of their Poisson homological groups and their Poissoncohomological groups. More precisely, under some assumptions, we obtain thePoincar\-e series of these Poisson homological groups and we compute explicitlythese Poisson cohomological groups, except the second group which seems morecomplicated to obtain.



Author: Serge Roméo Tagne Pelap

Source: https://arxiv.org/



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