symplectic geometry

higher symplectic geometry

geometry

differential geometry

almost symplectic structure, metaplectic structure, metalinear structure

symplectic form, n-plectic form

symplectic Lie n-algebroid

symplectic manifold

Poisson manifold, Poisson Lie algebroid

Poisson n-algebra

Courant Lie 2-algebroid

symplectic infinity-groupoid

symplectomorphism, symplectomorphism group

symplectic vector field, Hamiltonian vector field

symplectic gradient

Hamiltonian action, moment map

symplectic reduction, BRST-BV formalism

isotropic submanifold, Lagrangian submanifold, polarization

Hamiltonian mechanics

quantization

deformation quantization,

geometric quantization, higher geometric quantization

geometric quantization of symplectic groupoids

prequantum line bundle, prequantum circle n-bundle

quantomorphism group, quantomorphism n-group

Poisson bracket, Poisson algebra

Poisson bracket Lie n-algebra

Heisenberg Lie algebra, Heisenberg Lie n-algebra

Heisenberg group

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The analog in contact geometry of Lagrangian submanifolds in symplectic geometry.