Gluing and deformations of asymptotically cylindrical special Lagrangians

TL;DR

This paper develops a mathematical framework for gluing and deforming asymptotically cylindrical special Lagrangian submanifolds within Calabi-Yau manifolds, establishing a local diffeomorphism between deformation spaces.

Contribution

It introduces a well-defined gluing map for these submanifolds and proves it induces a local diffeomorphism in their deformation theory, with illustrative examples.

Findings

Existence of a well-defined gluing map.

The gluing map induces a local diffeomorphism.

Examples of applicable asymptotically cylindrical special Lagrangians.

Abstract

We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, prove that this gluing map defines a local diffeomorphism from matching pairs of deformations of asymptotically cylindrical special Lagrangians to deformations of special Lagrangians. We also give some examples of asymptotically cylindrical special Lagrangian submanifolds to which these results apply.