Lagrangian surgery
= Lagrangian surgery
{c}
Lagrangian surgery replaces two transverse local Lagrangian sheets by a smooth Lagrangian neck. For the standard planes $\mathbb R^n$ and $i\mathbb R^n$ in $\mathbb C^n$, a neck is obtained by following a curve between the two coordinate rays and multiplying it by points of $S^{n-1}$. In dimension four, resolving a double point attaches a one-handle to the source surface and lowers its <Euler characteristic> by two.