2017/03/31 by Joel Villatoro
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Computer science #Dirac (video compression format) #Homotopy and Cohomology in Algebraic Topology #Integrable system #Lie algebra #Manifold (fluid mechanics) #Mathematics #Morita therapy #Morphism #Physics #Poisson algebra #Poisson bracket #Poisson distribution #Poisson manifold #Pure mathematics #Quantum mechanics #Stack (abstract data type) #Symplectic geometry #math.DG #math.SG #msc:14A20 #msc:22A22 #msc:53D17
paper · pdf · doi:10.1007/s11005-017-1012-5
Made several improvements to the exposition and fixed typos
arxiv created 2017/09/28 · openalex publication_date 2017/10/13 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We associate to any integrable Poisson manifold a stack, i.e. a category fibered in groupoids over a site. The site in question has objects Dirac manifolds and morphisms pairs consisting of a smooth map and a closed 2-form. We show that two Poisson manifolds are symplectically Morita equivalent if and only if their associated stacks are isomorphic.