Mathematics – Differential Geometry
Scientific paper
2011-12-19
Mathematics
Differential Geometry
22pages, added some remark in Introduction
Scientific paper
The main result of this paper is surjectivity of a gluing of special Lagrangian submanifolds of dimension three. Joyce has proved that one can desingularize Clifford torus cone singularities by the gluing technique. Our main result is surjectivity of the gluing. A more precise statement is as follows. Consider a compact special Lagrangian submanifold of dimension three with one point singularity where it is tangent to the cone on the Clifford torus with multiplicity one. We may regard it as a varifold in Geometric Measure Theory. We find a coordinate system on a neighbourhood of it in the moduli space of special Lagrangian varifolds; the neighbourhood is a manifold with boundary. This is an analogue of Donaldson's theorem, which proves surjectivity of Taubes's gluing of anti-self-dual Yang-Mills connections.
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