In mathematics, a Lagrangian foliation or polarization is a

foliation In mathematics (differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition of ...

of a symplectic manifold, whose leaves are

Lagrangian submanifold In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M , equipped with a closed nondegenerate differential 2-form \omega , called the symplectic form. The study of symplectic manifolds is called sy ...

s. It is one of the steps involved in the

geometric quantization In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a wa ...

of a square-integrable functions on a symplectic manifold.

References

* Kenji FUKAYA
''Floer homology of Lagrangian Foliation and Noncommutative Mirror Symmetry''
(2000) {{topology-stub Symplectic geometry Foliations Mathematical quantization