Communications in Analysis and Geometry
Volume 25 (2017)
Surjectivity of a gluing construction in special Lagrangian geometry
Pages: 1019 – 1061
This paper is motivated by a relatively recent work by Joyce [12–16] in special Lagrangian geometry, but the basic idea of the present paper goes back to an earlier pioneering work of Donaldson  (explained also by Freed and Uhlenbeck ) 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.
Paper received on 2 February 2012.