Surjectivity of a gluing construction in special Lagrangian geometry

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 [5] (explained also by Freed and Uhlenbeck [7]) 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 [23].

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.

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Received 2 February 2012

Published 30 November 2017