Mathematical Sciences Classification System
53Dxx - Symplectic geometry, contact geometry
[See also 37Jxx, 70Gxx, 70Hxx]
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53D05Symplectic manifolds, general
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53D10Contact manifolds, general
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53D12Lagrangian submanifolds; Maslov index
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53D15Almost contact and almost symplectic manifolds
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53D17Poisson manifolds; Poisson groupoids and algebroids
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53D18Generalized geometries (à la Hitchin)
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53D20Momentum maps; symplectic reduction
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53D22Canonical transformations
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53D25Geodesic flows
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53D30Symplectic structures of moduli spaces
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53D35Global theory of symplectic and contact manifolds [See also 57Rxx]
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53D37Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]
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53D40Floer homology and cohomology, symplectic aspects
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53D42Symplectic field theory; contact homology
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53D45Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
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53D50Geometric quantization
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53D55Deformation quantization, star products
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53D99None of the above, but in this section