Symplectic geometry on symplectic knot spaces (Q870659)

The author studies the geometry and topology of the symplectic knot space \(\mathcal{K}^{\text{Sp}}(\Sigma , M)\) defined as the space of symplectic embeddings of an even-dimensional 2k oriented closed manifold \(\Sigma\) into a symplectic manifold \(M\) of dimension 2n. The space \(\mathcal{K}^{\text{Sp}}(\Sigma , M)\) carries a symplectic structure if \( k < n-1,\) cf. Theorem 2. Moreover, symplectic knot spaces can be realized as symplectic quotients (Theorem 6). Finally, the author investigates some symplectic geometry of the symplectic knot space, e.g. the correspondence between coisotropic submanifolds in \(M\) and Lagrangian ones in \(\mathcal{K}^{\text{Sp}}(\Sigma , M).\)