Homological mirror symmetry for the 4-torus

Abstract

We use the quilt formalism of Mau, Wehrheim, and Woodward to give a sufficient condition for a finite collection of Lagrangian submanifolds to split-generate the Fukaya category, and deduce homological mirror symmetry for the standard 4-torus. As an application, we study Lagrangian genus 2 surfaces Σ2⊂T4 of Maslov class zero, deriving numerical restrictions on the intersections of Σ2 with linear Lagrangian 2-tori in T4

Locations

• Duke Mathematical Journal - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View