Homological mirror symmetry for the four-torus

Details Homological mirror symmetry for the four-torus Homological mirror symmetry for the four-torus

2009-03-17

arxiv.org/abs/0903.3065v2

Mathematics

Symplectic Geometry

56 pages, 5 figures. The new version has been completely reorganised and includes longer explanations in the algebraic section

Scientific paper

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.

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