 Lagrangian surgery

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.