Regularization of almost complex structures and and gluing holomorphic discs to tori

TL;DR

This paper develops a method for removing singularities in almost complex structures and applies it to establish the existence of holomorphic discs attached to tori, advancing understanding in symplectic geometry.

Contribution

It introduces a singularity removal technique for almost complex structures and demonstrates the existence of boundary-attached holomorphic discs on tori.

Findings

Singularity removal for almost complex structures

Existence of global J-holomorphic discs with torus boundaries

Application to symplectic topology

Abstract

We prove a result on removing singularities of almost complex structures pulled back by a non-diffeomorphic map. As an application we prove the existence of global J-holomorphic discs with boundaries attached to real tori.