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Mathematical Sciences Classification System

53Dxx - Symplectic geometry, contact geometry
[See also 37Jxx, 70Gxx, 70Hxx]

• 8
  53D05
  Symplectic manifolds, general
• 8
  53D10
  Contact manifolds, general
• 11
  53D12
  Lagrangian submanifolds; Maslov index
• 53D15
  Almost contact and almost symplectic manifolds
• 11
  53D17
  Poisson manifolds; Poisson groupoids and algebroids
• 53D18
  Generalized geometries (à la Hitchin)
• 8
  53D20
  Momentum maps; symplectic reduction
• 53D22
  Canonical transformations
• 4
  53D25
  Geodesic flows
• 1
  53D30
  Symplectic structures of moduli spaces
• 6
  53D35
  Global theory of symplectic and contact manifolds [See also 57Rxx]
• 2
  53D37
  Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]
• 14
  53D40
  Floer homology and cohomology, symplectic aspects
• 1
  53D42
  Symplectic field theory; contact homology
• 9
  53D45
  Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
• 6
  53D50
  Geometric quantization
• 6
  53D55
  Deformation quantization, star products
• 1
  53D99
  None of the above, but in this section