Self-Similarity of Poisson structures on tori
We study the group of diffeomorphisms of a 3-dimensional Poisson torus which preserve the Poisson structure up to a constant multiplier, and the group of similarity ratios.
Several cohomology algebras connected with Poisson structure.
Shoikhet's conjecture and Duflo isomorphism on (co)invariants.
Singular Poisson reduction of cotangent bundles.
We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.
Singularities of Poisson and Nambu structures
Some liftings of Poisson structures to Weil bundles
We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.
Stability of higher order singular points of Poisson manifolds and Lie algebroids
We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...
Structures de Poisson sur les variétés algébriques de dimension trois