# Real Lagrangians in Calabi-Yau Threefolds

## TL;DR

This paper computes the mod 2 cohomology of real Lagrangians in Calabi-Yau threefolds using torus fibrations, revealing a connection to divisor class squaring in mirror Calabi-Yaus.

## Contribution

It introduces a method to compute cohomology of real Lagrangians in Calabi-Yau threefolds via a long exact sequence and identifies the connecting homomorphism with divisor class squaring.

## Key findings

- Computed mod 2 cohomology groups of real Lagrangians.
- Identified the connecting homomorphism as squaring divisor classes.
- Linked the cohomology to mirror symmetry via divisor classes.

## 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 Casta\~{n}o-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.