On a Lagrangian Version of the Lagrangian Whitney Trick

Abstract

We write down a formula for a model case by which the Lagrangian Whitney trick is realized, that is, a process to remove a pair of transverse intersection points of a Lagrangian immersion by a homotopy through Lagrangian immersions. The formula gives a homotopy with a compact support assuming the model satisfies so called an area-capacity condition. An observation is made regarding its application, which is more amusing than significant in its nature.