Clean-circle resolution of a Lagrangian surface immersion
= Clean-circle resolution of a Lagrangian surface immersion
Perturb a clean self-intersection circle of a <Lagrangian immersion> by a <Morse function> on $S^1$. Its minimum and maximum give two transverse double points. Resolving both by <Lagrangian surgery> adds two one-handles and changes the Euler characteristic by $-4$. One neck may be glued with the orientation-reversing choice, so the resolved surface is nonorientable.