= Lagrangian lift through circle reduction
{title2=$\widetilde L=\pi^{-1}(L)$}
At a regular free <circle group> level of a <moment map>, the inverse image of a <Lagrangian submanifold> of the reduced space is a <Lagrangian submanifold> of the original space. Its restricted <symplectic form> is the pullback of the reduced form and hence vanishes. Its dimension is one more than that of the reduced Lagrangian, exactly half the ambient dimension. It is a <circle bundle> over the original Lagrangian.
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