New York Journal of Mathematics
Volume 13 (2007) 97-106


Jae-Hyouk Lee

Symplectic geometry on symplectic knot spaces

Published: March 10, 2007
Keywords: Symplectic knot space, symplectic reduction, coisotropic submanifold, Lagrangian submanifold, almost complex submanifold, holomorphic curve
Subject: 53C38, 53D20, 53D30, 53D12, 54C99

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.

Author information

Department of Mathematics, Washington University in St. Louis, St. Louis, MO 63130, U.S.A.