## Duke Mathematical Journal

### 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 $\Sigma_2 \subset T^4$ of Maslov class zero, deriving numerical restrictions on the intersections of $\Sigma_2$ with linear Lagrangian $2$-tori in $T^4$

#### Article information

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

Dates
First available in Project Euclid: 20 April 2010

http://projecteuclid.org/euclid.dmj/1271783595

Digital Object Identifier
doi:10.1215/00127094-2010-015

Mathematical Reviews number (MathSciNet)
MR2654219

Zentralblatt MATH identifier
05708809

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

#### Citation

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. http://projecteuclid.org/euclid.dmj/1271783595.

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