Homological mirror symmetry for the four-torus
Symplectic Geometry
2019-12-19 v2 Algebraic Geometry
Abstract
We use the quilt formalism of Mau-Wehrheim-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 two surfaces of Maslov class zero, deriving numerical restrictions on the intersections of such a surface with linear Lagrangian 2-tori in in the 4-torus.
Keywords
Cite
@article{arxiv.0903.3065,
title = {Homological mirror symmetry for the four-torus},
author = {Mohammed Abouzaid and Ivan Smith},
journal= {arXiv preprint arXiv:0903.3065},
year = {2019}
}
Comments
56 pages, 5 figures. The new version has been completely reorganised and includes longer explanations in the algebraic sections