Nonlinearizability of certain Poisson structures near a symplectic leaf

2004/06/29 by Benjamin Lent Davis, B. L. Davis, Davis, Benjamin Lent +3
Mathematics · Physics and Astronomy · #53Cxx #70G45 #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.SG #msc:53Cxx #msc:70G45

paper · pdf · doi:10.48550/arxiv.math/0406611

corrected typos

openalex publication_date 2004/06/29 · arxiv created 2005/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an intrinsic proof that Vorobjev's first approximation of a Poisson manifold near a symplectic leaf is a Poisson manifold. We also show that Conn's linearization results cannot be extended in Vorobjev's setting.

Citations

• Normal forms of Poisson structures near a symplectic leaf

Related

• Poisson Equivalence over a Symplectic Leaf
• Normal forms of Poisson structures near a symplectic leaf
• Poisson geometry around Poisson submanifolds
• A geometric approach to Conn's linearization theorem
• Coupling Tensors and Poisson Geometry Near a Single Symplectic Leaf