Equivariant Poisson Cohomology and a Spectral Sequence Associated with a Moment Map

Details Equivariant Poisson Cohomology and a Spectral Sequence Associated with a Moment Map Equivariant Poisson Cohomology and a Spectral Sequence Associated with a Moment Map

1996-11-11

arxiv.org/abs/dg-ga/9611002v2

Mathematics

Differential Geometry

AMS-LaTeX, 32 pages

Scientific paper

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the $E_2$-term equal to the tensor product of the cohomology of the Lie algebra and the equivariant Poisson cohomology of the manifold. The latter is defined as the equivariant cohomology of the multi-vector fields made into a G-differential complex by means of the momentum mapping. An extensive introduction to equivariant cohomology of G-differential complexes is given including some new results and a number of examples and applications are considered.

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