= Marsden-Weinstein theorem
{c}
{title2=$\mu^{-1}(c)/G$}
For a <Hamiltonian group action>, let $c$ be a <regular value> of the <moment map> fixed by the <coadjoint action>, and assume the action on $\mu^{-1}(c)$ is free and proper. The quotient is a <symplectic manifold> of dimension $\dim M-2\dim G$. Its unique reduced <symplectic form> is characterized by $\pi^*\omega_c=\iota^*\omega$, where $\iota$ includes the level set and $\pi$ is the quotient projection. The kernel of the restricted two-form consists precisely of the orbit directions. More general noncentral levels use their stabilizer group; the stated central-level version suffices for <circle group> reduction.
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