Mathematical Sciences Classification System

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

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

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