Suppose there is a closed differential form whose periods lie inside an additive subgroup of the real numbers e.g the integers or the rational numbers.(adsbygoogle = window.adsbygoogle || []).push({});

Does this form determine a cohomology class with coefficients in this subgroup? I think this follows from the universal coefficient theorem.

Conversely given a non-torsion cohomology class (on a smooth manifold)with coefficients in one of the subgroups does there correspond a closed differential form with the same periods?

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# A Question about de Rham's Theorem

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