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Better spelling "DeRham", not derham... I can't figure out how to change this... moderators? The cohomology of the complex of differential forms on a smooth manifold with differential given by exterior derivative.

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Can one make sense of de Rham cohomology for the complement of a (dense) irrational flow on ...

The torus $T^2$ is the quotient of ${\mathbf R}^2$ by ${\mathbf Z}^2$. I denote by $z = [x,y]$ the class of $(x,y) \in {\mathbf R}^2$. I am used to denote $\Delta_\alpha \subset T^2$ what you denote b …
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