I want to show that the $S^2$ isn't diffeomorphic to complex torus.I just want to understand why $H_{dR}^1(T) \neq 0$. If someone could explain it in details that would be nice since we didn't cover the details of calculation in my class as much as I wanted to.
2026-04-09 14:32:03.1775745123
Showing that $H_{dR}^1(T) \neq 0$ where $T = \mathbb{C} / ( \mathbb{Z} + \mathbb{Z}*i)$
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