On Constructing Special Lagrangian Submanifolds by Gluing

TL;DR

This paper applies a previously established gluing theorem to construct new special Lagrangian submanifolds in Calabi-Yau 3-folds by smoothing intersections of multiple Lagrangians, expanding the methods for generating such structures.

Contribution

It demonstrates the application of a gluing theorem to more general intersecting special Lagrangians, enabling the construction of new smooth submanifolds from complex intersections.

Findings

Successfully constructed a smooth special Lagrangian from five intersecting RP^3's.

Extended the gluing theorem to more general intersection configurations.

Provided explicit example in a quintic Calabi-Yau manifold.

Abstract

The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special Lagrangian submanifold. In this paper we will show that this theorem can be applied to more general cases where different special Lagrangians are intersecting and gives a way of constructing new special Lagrangian submanifolds. As an example we will show that a smooth special Lagrangian submanifold can be obtained from five copies of RP^3 intersecting pairwise in a quintic.