List questions from homology-cohomology

Published on 27 Mar 2026 - 15:19

190

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Hatcher's geometric interpretation of cochains for surfaces

Published on 27 Nov 2018 - 7:27

178

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Showing that any central group extension of a finite group $G$ by the trivial $G$-module $\mathbb Q$ is a semidirect product

Published on 25 Mar 2026 - 4:43

156

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Reference for Hodge decomposition for flag variety

Published on 26 Mar 2026 - 1:02

509

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If one has two path-connected spaces, must a map induced by $f:X\to Y$ be an isomorphism on $H_0(X)\to H_0(Y)$?

Published on 01 Dec 2018 - 4:39

904

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Classification of double coverings and $H^1(X ; \mathbb{Z}/2\mathbb{Z})$

Published on 25 Mar 2026 - 19:05

724

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Homology groups with different complexes

Published on 25 Mar 2026 - 9:32

618

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Construct compact space with some homology group not finitely generated

Published on 02 Dec 2018 - 19:41

117

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Understanding why the Adams Spectral Sequence works

Published on 25 Mar 2026 - 9:50

107

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On cohomology of flasque sheaves of abelian groups

Published on 25 Mar 2026 - 6:07

808

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Formality of commutative differential graded algebras

Published on 25 Mar 2026 - 1:29

240

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Proof of Borsuk-Ulam Theorem using singular Homology

Published on 05 Dec 2018 - 19:19

1.2k

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Homological algebra using nonabelian groups

Published on 31 Mar 2026 - 4:18

489

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Kähler manifolds are formal

Published on 27 Mar 2026 - 17:06

784

Views

Reference for algebro-geometric definition of the $\cup$-product in (sheaf) cohomology.

Published on 25 Mar 2026 - 6:07

List Question

Cohomology of n-sphere minus k discs

Hatcher's geometric interpretation of cochains for surfaces

Showing that any central group extension of a finite group $G$ by the trivial $G$-module $\mathbb Q$ is a semidirect product

Reference for Hodge decomposition for flag variety

If one has two path-connected spaces, must a map induced by $f:X\to Y$ be an isomorphism on $H_0(X)\to H_0(Y)$?

Classification of double coverings and $H^1(X ; \mathbb{Z}/2\mathbb{Z})$

Homology groups with different complexes

Construct compact space with some homology group not finitely generated

Understanding why the Adams Spectral Sequence works

On cohomology of flasque sheaves of abelian groups

Formality of commutative differential graded algebras

Proof of Borsuk-Ulam Theorem using singular Homology

Homological algebra using nonabelian groups

Kähler manifolds are formal

Reference for algebro-geometric definition of the $\cup$-product in (sheaf) cohomology.

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