Real Lagrangians in Calabi-Yau Threefolds

Abstract

We compute the mod $2$ cohomology groups of real Lagrangians in Calabi-Yau threefolds using well-behaved torus fibrations constructed by Gross. To do this we study a long exact sequence introduced by Castaño-Bernard and Matessi, which relates the cohomology of the Lagrangians to the cohomology of the Calabi-Yau. We show that the connecting homomorphism in this sequence is given by the map squaring divisor classes in the mirror Calabi-Yau.

31 pages, 8 figures. Improved exposition of Appendix A and corrected Example 4.11. Minor adjustments throughout