53XX 


Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} 

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 
GromovWitten 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 