Symplectic GeometryLecture 12More on moment mapsReview: symplectic actions of a group.Review: Weakly Hamiltonian actionsReview: Moment maps.Review: Hamiltonian actions.Review: Exact symplectic actions.Review: Induced cotangent actions.The unitary group.If then=The moment map for U(n) acting on C .nThe maximal torus of U(n) .The image of the moment map.Complex representations of a torus.Weights.The moment map.Preview.Normalization near a fixed point.The cone near a fixed point.The local cone at a general point.A circle action on C .nThe spheres.The spheres are co-isotropicThe foliation is a fibration.The symplectic structure on projective space.The derivative of the moment map.The evaluation map and its transpose.The moment map and the evaluation map.The kernel of the derivative of the moment map.A transitive Hamiltonian space covers a coadjoint orbit.The restriction of the symplectic form to an orbit.The Kostant-Souiau form, 1.The Kostant-Souiau form, 2.The Kostant-Souiau form, 3.The Kostant-Souiau form, 4.The Kostant-Souriau theorem.The image of the derivative of the moment map.The stabilizer