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A Lagrangian submanifold of a $2n$-dimensional symplectic manifold is an $n$-dimensional submanifold $L$ satisfying $\omega {|}_L=0$. The symplectic form identifies its normal bundle with its cotangent bundle.

The Weinstein neighborhood theorem states that if $L$ is a compact Lagrangian submanifold of $(M,\omega )$, then neighborhoods of $L$ in $M$ and of the zero section in its cotangent bundle $T^{\ast }L$ are symplectomorphic. The symplectomorphism restricts to the identity on $L$, and the canonical form on $T^{\ast }L$ is taken with the sign matching the chosen convention.