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Israel Journal of Mathematics

, Volume 106, Issue 1, pp 133–155 | Cite as

The canonical spectral sequences for poisson manifolds

  • Marisa Fernández
  • Raúl Ibáñez
  • Manuel de León
Article

Abstract

For a compact symplectic manifoldM of dimension 2n, Brylinski proved that the canonical homology groupH k can (M) is isomorphic to the de Rham cohomology groupH 2n-k (M), and the first spectral sequence {E r (M)} degenerates atE 1(M). In this paper, we show that these isomorphisms do not exist for an arbitrary Poisson manifold. More precisely, we exhibit an example of a five-dimensional compact Poisson manifoldM 5 for whichH 1 can (M 5) is not isomorphic toH 4(M 5), andE 1(M 5) is not isomorphic toE 2(M 5).

Keywords

Poisson Bracket Spectral Sequence Symplectic Manifold Poisson Manifold Poisson Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1998

Authors and Affiliations

  • Marisa Fernández
    • 1
  • Raúl Ibáñez
    • 1
  • Manuel de León
    • 2
  1. 1.Departmento de Matemáticas, Facultad de CienciasUniversidad del País VascoBilbaoSpain
  2. 2.Instituto de Matemáticas y Física FundamentalConsejo Superior de Investigaciones CientíficasMadridSpain

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