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In mathematics, a Fedosov manifold is a symplectic manifold with a compatible torsion-free connection, that is, a triple , where is a symplectic manifold , and ∇ is a symplectic torsion-free connection on M . {\displaystyle M.} = ω + ω for all vector fields X,Y,Z ∈ Γ. In other words, the symplectic form is parallel with respect to the connection, i.e., its covariant derivative vanishes.] Note that every symplectic manifold admits a symplectic torsion-free connection. Cover the manifold with Darboux charts and on each chart define a connection ∇ with Christoffel symbol Γ j k i = 0 {\displaystyle \Gamma _{jk}^{i}=0}. Then choose a partition of unity and glue the local connections together to a global connection which still preserves the symplectic form. The famous result of Boris Vasilievich Fedosov gives a canonical deformation quantization of a Fedosov manifold.