Lagrangian immersion

A Lagrangian immersion is an immersion $\iota :L^n\to (M^{2n},\omega )$ satisfying ${\iota }^{\ast }\omega =0$.

If ${\gamma }_i:L_i\to (M_i,{\omega }_i)$ are one-dimensional immersed curves in symplectic surfaces, thenis a Lagrangian immersion. A double point of one factor times the other curve becomes a clean self-intersection circle.

A clean Lagrangian intersection is a clean intersection between two local Lagrangian sheets. A small exact perturbation of one sheet near a compact clean component replaces the intersection by the critical points of a Morse function on that component.