Structure of the image of (pseudo)-holomorphic discs with totally real boundary condition

Abstract

In this paper, we prove that the image of a (pseudo)-holomorphic map from the unit disc with its boundary on a given totally real submanifold is represented as a finite union of the images of "simple" discs allowing multiplicity with boundaries on the same totally real submanifold. This in particular fills a technical gap in relation to the Fredholm and the intersection theory of Gromov's (pseudo)holomorphic discs, which has been present in the literature on the applications of pseudo-holomorphic discs.