Explanation of De Rham Cohomology
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Intuitive Approach to de Rham Cohomology
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Precise connection between complexification of $\mathfrak{su}(2)$, $\mathfrak{so}(1,3)$ and $\mathfrak{sl}(2, \mathbb{C})$
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set of almost complex structures on $\mathbb R^4$ as two disjoint spheres
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cup product in cohomology ring of a suspension
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Prove the group of all real translations and all glide reflections with axis$R$ is isomorphic to $\{1,-1\}\times \mathbb R$
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How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
6843
Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$
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Prerequisite for Milnor Topology from a Differential Viewpoint
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Homology of $S^1 \times (S^1 \vee S^1)$
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Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
140003
Why only consider Dolbeault cohomology?
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relative homology is the reduced homology of the quotient
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Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
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Why is that $\widehat{\mathbb{R}/\mathbb{Z}}\cong\mathbb{Z}$?
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Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
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$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
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Proof that two spaces that are homotopic have the same de Rham cohomology