For the special case of a rectangular at torus, we present and prove DeRham's Theorem, which says that cohomology is given by closed differential forms modulo exact forms.
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Eric M. Katerman, DeRham Cohomology of the Rectangular Torus, Furman University Electronic Journal of Undergraduate Mathematics, 11 (2016), 1-3. Available at: https://scholarexchange.furman.edu/fuejum/vol11/iss1/1