Duke Mathematical Journal

Homological mirror symmetry for the 4-torus

Mohammed Abouzaid and Ivan Smith

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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 Σ2T4 of Maslov class zero, deriving numerical restrictions on the intersections of Σ2 with linear Lagrangian 2-tori in T4

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Duke Math. J. Volume 152, Number 3 (2010), 373-440.

First available in Project Euclid: 20 April 2010

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Zentralblatt MATH identifier

Primary: 14J32: Calabi-Yau manifolds
Secondary: 53D40: Floer homology and cohomology, symplectic aspects


Abouzaid, Mohammed; Smith, Ivan. Homological mirror symmetry for the 4-torus. Duke Math. J. 152 (2010), no. 3, 373--440. doi:10.1215/00127094-2010-015. https://projecteuclid.org/euclid.dmj/1271783595

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