Lectures on Special Lagrangian Submanifolds
Nigel Hitchin
TL;DR
This paper explores special Lagrangian submanifolds within Calabi-Yau manifolds, focusing on their moduli spaces, the role of gerbes in three dimensions, and implications for mirror symmetry in string theory.
Contribution
It introduces the concept of gerbes to describe features of the Strominger-Yau-Zaslow approach to mirror symmetry in the context of special Lagrangian submanifolds.
Findings
Development of the gerbe framework for three-dimensional cases
Insights into the moduli space structure of special Lagrangian submanifolds
Connections established between geometry and string theory applications
Abstract
These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer an appropriate language for describing many significant features of the Strominger-Yau-Zaslow approach to mirror symmetry.
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Taxonomy
TopicsGeometry and complex manifolds · Black Holes and Theoretical Physics · Geometric Analysis and Curvature Flows