Restriction of the moment map to certain non-Lagrangian submanifolds
  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. 
Michael Otto