Contents

• Poisson Geometry
  • Poisson algebra
  • Poisson manifolds
  • The sharp map
  • The symplectic foliation
  
  
• Schouten-Nijenhuis bracket
  • Lie-Poisson bracket
  • Schouten-Nijenhuis bracket
    • Schouten-Nijenhuis bracket computations
    • Lichnerowicz definition of the Schouten-Nijenhuis bracket
    • Jacobi condition and Schouten-Nijenhuis bracket
    • Compatible Poisson tensors
    • Koszul's formula
  • Poisson homology
  
  
• Poisson maps
  • Poisson maps
  • Poisson submanifolds
  • Coinduced Poisson structures
  • Completeness
  
  
• Poisson cohomology
  • Modular class
  • Computation for Poisson cohomology
  
  
• Poisson homology
  • Poisson homology and modular class
  
  
• Coisotropic submanifolds
  • Poisson Morita equivalence
  • Dirac structures
  
  
• Poisson Lie groups
  • Poisson Lie groups
  • Lie bialgebras
  • Manin triples
  
  
• Poisson actions
  • Poisson actions
  • Poisson homogeneous spaces
  • Dressing actions
  
  
• Quantization
  • Introduction
  • Duality
  • Local, global, special quantizations
  • Real structures
  • Dictionary
  • Quantum subgroups
  • Quantum homogeneous spaces
  • Coisotropic creed
  
  
• Bibliography