Symplectic geometry on symplectic knot spaces

Symplectic knot spaces are the spaces of symplectic subspaces in a symplectic manifold M. We introduce a symplectic structure and show that the structure can be also obtained by the symplectic quotient method. We explain the correspondence between coisotropic submanifolds in M and Lagrangians in the symplectic knot space. We also define an almost complex structure on the symplectic knot space, and study the correspondence between almost complex submanifolds in M and holomorphic curves in the symplectic knot space.