Les variétés de Poisson et leurs algèbres de Lie associées

  title={Les vari{\'e}t{\'e}s de Poisson et leurs alg{\`e}bres de Lie associ{\'e}es},
  author={Andr{\'e} Lichnerowicz},
  journal={Journal of Differential Geometry},


We study the “twisted” Poincaré duality of smooth Poisson manifolds, and show that, if the modular symmetry is semisimple, that is, the modular vector is diagonalizable, there is a mixed complex

A local Torelli theorem for log symplectic manifolds

We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the

On Poisson structures of hydrodynamic type and their deformations

Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type systems, are one of the most important classes of nonlinear partial differential equations in the

Normal forms of Poisson structures

These notes arise from a minicourse given by the two authors at the Summer School on Poisson Geometry, ICTP, 2005. The main reference is our recent monograph “Poisson structures and their normal

An introduction to some novel applications of Lie algebra cohomology in mathematics and physics

This paper has been partially supported by a research grant from the MEC, Spain (PB96-0756). J. C. P. B. wishes to thank the Spanish MEC and the CSIC for an FPI grant.

An introduction to some novel applications of Lie algebra cohomology and physics

After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential

Basic forms and Morse–Novikov cohomology of Lie groupoids

  • Hao Ding
  • Mathematics
    Mathematische Nachrichten
  • 2018
Given a basic closed 1‐form on a Lie groupoid G , the Morse–Novikov cohomology groups Hθn(G) are defined in this paper. They coincide with the usual de Rham cohomology groups HdRn(G) when θ is exact

Morse-Novikov Cohomology for Blow-ups of Complex Manfiolds

We define the weight {\theta}-sheaf R_{X,\theta} and reinterpret Morse-Novikov cohomology via sheaf theory. We establish a theorem of Leray-Hirsch type for Morse-Novikov cohomology. Eventually, using

Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor

In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold $(M, \pi)$ to its tangent bundle $(TM, \pi_{TM})$ are also Poisson. We use this fact to