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arXiv:0903.3065math.SG

Homological mirror symmetry for the four-torus

Mohammed Abouzaid, Ivan Smith

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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.

arXiv comments
56 pages, 5 figures. The new version has been completely reorganised and includes longer explanations in the algebraic sections
Journal reference
Duke Math. J. 152, no. 3 (2010), 373-440
DOI
doi:10.1215/00127094-2010-015
Subjects
math.SGSymplectic Geometry math.AGAlgebraic Geometry

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  1. Show HN: Arxiv Vanity – Read academic papers from Arxiv as responsive web pages 1 comment

    • Unfortunately it's failing on first things I tried with a not-so-helpful error message: https://www.arxiv-vanity.com/papers/1608.04012/ https://www.arxiv-vanity.com/papers/0903.3065/ Also a lot of MathJax failures (maybe Latex variables names?)…

      dbranesView on HNParent context

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