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Why is every top form on a non-compact manifold exact? (without invoking Poincare duality)

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#algebraic-topology #homology-cohomology #differential-forms #de-rham-cohomology
863
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The Hodge diamond of a Calabi-Yau Fourfold

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#differential-geometry #algebraic-geometry #homology-cohomology #de-rham-cohomology
2.3k
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How is de Rham cohomology useful?

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#smooth-manifolds #de-rham-cohomology
567
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de Rham cohomology with compact support isomorphic to $\mathbb{R}$

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#differential-topology #differential-forms #de-rham-cohomology
279
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Do the Generators of integral de Rham Cohomology always integrate to 1?

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#differential-geometry #algebraic-topology #homology-cohomology #differential-forms #de-rham-cohomology
70
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Example 24.4 Tu's An Introduction to Manifolds

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#proof-explanation #smooth-manifolds #de-rham-cohomology
169
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Relation between Hochschild homology and cohomology

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#homology-cohomology #differential-forms #symplectic-geometry #de-rham-cohomology #hochschild-cohomology
24
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What is a good reference to cite for the definition of forms in terms of germs of functions?

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#reference-request #differential-forms #de-rham-cohomology #germs
70
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An action of Lie group and cohomology

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#lie-groups #smooth-manifolds #group-actions #de-rham-cohomology
80
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If $X$ is closed then $JX$ is closed

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#algebraic-topology #homology-cohomology #riemann-surfaces #complex-manifolds #de-rham-cohomology
77
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Functoriality of twisted de Rham Cohomology

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#differential-forms #vector-bundles #functors #de-rham-cohomology
289
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First sheaf cohomology of closed 1-forms on a homogeneous space

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#algebraic-geometry #lie-groups #differential-forms #sheaf-cohomology #de-rham-cohomology
525
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De Rham cohomology of $S^1$ with compact supports (Bott/Tu)

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#differential-geometry #algebraic-topology #differential-topology #homology-cohomology #de-rham-cohomology
224
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Tu's An Introduction to Manifolds - Section 26.2 Cohomology of a circle, tabular form.

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#manifolds #de-rham-cohomology
102
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algebraic de Rham cohomology of blowup of relative line

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#algebraic-geometry #blowup #de-rham-cohomology #positive-characteristic

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