Restriction of the moment map to certain non-Lagrangian submanifolds

Details Restriction of the moment map to certain non-Lagrangian submanifolds Restriction of the moment map to certain non-Lagrangian submanifolds

2006-09-20

arxiv.org/abs/math/0609541v1

Mathematics

Symplectic Geometry

14 pages

Scientific paper

Consider a Hamiltonian torus action on a connected symplectic manifold M for which the associated moment map Phi is proper in some sense. Let Q be a closed submanifold of M. We show that under certain local conditions on Q one has Phi(Q)=Phi(M). We apply this result in the special case that Q arises as the fixed point set of some involution on M which is not necessarily antisymplectic.

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