2005/03/28 by Yuriǐ Vorobjev, Yurii Vorobjev, Vorobjev, Yurii
Mathematics · Medicine · #53C05 #53D17 #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG) #math.SG #msc:53C05 #msc:53D17
paper · pdf · doi:10.48550/arxiv.math/0503628
Latex file, 52p, minor corrections
openalex publication_date 2005/03/28 · arxiv created 2005/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the equivalence of Poisson structures around a given symplectic leaf of nonzero dimension. Some criteria of Poisson equivalence are derived from a homotopy argument for coupling Poisson structures. In the case when the transverse Lie algebra of the symplectic leaf is semisimple of compact type, we show that an obstruction to the linearizability is the cohomology class of a Casimir 2-cocycle. This allows us to obtain a semilocal analog of the Conn linearization theorem and to clarify examples of nonlinearizable Poisson structures due to \citeDW.