List questions from homology-cohomology

Published on 13 May 2026 - 16:39

642

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Is the cohomology of a stalk the same as the stalk of the cohomology sheaf?

Published on 05 May 2026 - 6:00

217

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$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

Published on 10 May 2026 - 14:54

240

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First cohomology of topological spaces with non abelian coefficients

Published on 10 May 2026 - 23:51

384

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If integrals of pullbacks of a form only depend on the boundary values, is it exact?

Published on 10 May 2026 - 15:02

268

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Example of a nongraded chain complex

Published on 11 May 2026 - 16:49

341

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The Converse of Poincare Lemma

Published on 10 May 2026 - 20:14

1.7k

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Cohomology of blow-up

Published on 03 May 2026 - 2:41

1.8k

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Cohomology of projective bundle only depends on base and fiber?

Published on 29 Apr 2026 - 12:47

335

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Finite generatedness of singular cohomology of compact manifolds

Published on 10 May 2026 - 17:16

118

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Unclear step on the calculation of a homology group.

Published on 11 May 2026 - 9:10

77

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Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

Published on 07 May 2026 - 15:40

266

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Finding chains with a given boundary

Published on 29 Apr 2026 - 12:19

176

Views

How to think of the Kodaira dimension of surface

Published on 10 May 2026 - 17:16

520

Views

References for classifying spaces and cohomology of classifying spaces

Published on 11 May 2026 - 16:34

List Question

Defining a sort of "cohomology"

Is the cohomology of a stalk the same as the stalk of the cohomology sheaf?

$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

First cohomology of topological spaces with non abelian coefficients

If integrals of pullbacks of a form only depend on the boundary values, is it exact?

Example of a nongraded chain complex

The Converse of Poincare Lemma

Cohomology of blow-up

Cohomology of projective bundle only depends on base and fiber?

Finite generatedness of singular cohomology of compact manifolds

Unclear step on the calculation of a homology group.

Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

Finding chains with a given boundary

How to think of the Kodaira dimension of surface

References for classifying spaces and cohomology of classifying spaces

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