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Local structure of Poisson manifolds
  • A. Weinstein
  • Mathematics
    Lectures on Poisson Geometry
  • 14 September 2021
Varietes de Poisson et applications. Decomposition. Structures de Poisson lineaires. Approximation lineaire. Systemes hamiltoniens. Le probleme de linearisation. Groupes de fonction, realisations et…
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Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
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Poisson Geometry with a 3-Form Background
We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable…
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Symplectic manifolds and their lagrangian submanifolds
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Lectures on Symplectic Manifolds
Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations,…
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Geometric Models for Noncommutative Algebras
UNIVERSAL ENVELOPING ALGEBRAS Algebraic constructions The Poincare-Birkhoff-Witt theorem POISSON GEOMETRY Poisson structures Normal forms Local Poisson geometry POISSON CATEGORY Poisson maps…
Contact surgery and symplectic handlebodies
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Integration of twisted Dirac brackets
Given a Lie groupoid G over a manifold M, we show that multiplicative 2-forms on G relatively closed with respect to a closed 3-form phi on M correspond to maps from the Lie algebroid of G into T* M…
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Coisotropic calculus and Poisson groupoids
Lagrangian submanif olds play a special role in the geometry of symplectic manifolds. From the point of view of quantization theory, or simply a categorical approach to symplectic geometry [Gu-S2],…
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The modular automorphism group of a Poisson manifold
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