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I'm a new users. I'd like to calculate the De Rham cohomology of euclidean space $\mathbb{R}^{3}$ without a circle $\mathbb{S}^{1}$. I don't have idea how to proceed! I saw the answer given to this question here but I don't understand nothing. The only tools that I know are the Mayer-Vietoris sequence and the equivalence of cohomology of homotopic manifolds. I also know the De Rham cohomology of n-dimensional sphere $\mathbb{S}^{n}$ and the De Rham cohomology of projective spaces. How can I proceed? Should I use Mayer-Vietoris? Or should I find an homotopy between $M=\mathbb{R}^{3}$ \ $\mathbb{S}^{1}$ and another manifold simplier to calculate?

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