53Dxx Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
- 53D05 Symplectic manifolds, general (1)
- 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