Surjectivity of a Gluing Construction in Special Lagrangian Geometry

TL;DR

This paper establishes the surjectivity of a gluing construction in special Lagrangian geometry, drawing parallels to Donaldson's work in gauge theory, thereby advancing understanding of moduli space structures.

Contribution

It proves the surjectivity of Joyce's gluing construction in a specific case, providing a local description near boundary points of moduli spaces in special Lagrangian geometry.

Findings

Identifies a neighborhood of a boundary point in the moduli space.

Shows local similarity to Donaldson's results in gauge theory.

Establishes surjectivity of Joyce's gluing construction in a simple case.

Abstract

This paper is motivated by a relatively recent work by Joyce in special Lagrangian geometry, but the basic idea of the present paper goes back to an earlier pioneering work of Donaldson in Yang--Mills gauge theory; Donaldson discovered a global structure of a (compactified) moduli space of Yang--Mills instantons, and a key step to that result was the proof of surjectivity of Taubes' gluing construction. In special Lagrangian geometry we have currently no such a global understanding of (compactified) moduli spaces, but in the present paper we determine a neighbourhood of a `boundary' point. It is locally similar to Donaldson's result, and in particular as Donaldson's result implies the surjectivity of Taubes' gluing construction so our result implies the surjectivity of Joyce's gluing construction in a certain simple case.