Let fix an arbitraly lattice of $\mathbb{C}$ and call it Λ.
How to prove $H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ is isomorphic to the lattice $\Lambda$ via the map $f:\gamma \mapsto \int_\gamma dz$ ?
If once the map $f$ is proved to be surjective, I finish the proof. I already proved this map is well defined, hom, inj.
For arbitrary $nω1＋mω2$ from $Λ$, what is the original image of $f$?
Thank you for your help.