List questions from homology-cohomology

Published on 16 Apr 2026 - 15:33

507

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Higher homology groups of knots and links

Published on 11 Apr 2026 - 12:11

4k

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relative homology is the reduced homology of the quotient

Published on 13 Apr 2026 - 10:51

377

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Orientation of points in cell complexes

Published on 10 May 2026 - 18:01

1.4k

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Understanding Hatcher's cup product examples

Published on 11 Apr 2026 - 16:54

119

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reference request: covering spaces classification with $S_i$-Cech Cohomology

Published on 17 Apr 2026 - 12:24

230

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Examples of odd dimensional rationally acyclic closed manifolds.

Published on 13 Apr 2026 - 11:41

139

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$\tilde{H}^n(X,\mathbb{Z})\cong {H}^n(X,\mathbb{Z})\otimes_{\mathbb{Z}}\mathbb{R}$?

Published on 10 May 2026 - 22:09

144

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$\mathcal{H}^q$ is a locally constant presheaf

Published on 10 May 2026 - 15:51

284

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Rational cohomology ring of complex Grassmannian.

Published on 11 Apr 2026 - 20:35

131

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Cobordant 1-manifolds are homologous?

Published on 13 May 2026 - 5:44

53

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Relation of $\mathbb{Z}_2$-cohomology and interger cohomology

Published on 13 May 2026 - 1:52

303

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Show a map in cohomology is trivial

Published on 13 Apr 2026 - 14:09

324

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Understanding homologies of pairs and induced maps

Published on 12 Apr 2026 - 12:20

88

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Filling a hole by eliminating a homology class

Published on 11 Apr 2026 - 15:34

List Question

Does there exist $f:M \rightarrow S^n$ s.t. $f_{*}([M])=[S^n]$?

Higher homology groups of knots and links

relative homology is the reduced homology of the quotient

Orientation of points in cell complexes

Understanding Hatcher's cup product examples

reference request: covering spaces classification with $S_i$-Cech Cohomology

Examples of odd dimensional rationally acyclic closed manifolds.

$\tilde{H}^n(X,\mathbb{Z})\cong {H}^n(X,\mathbb{Z})\otimes_{\mathbb{Z}}\mathbb{R}$?

$\mathcal{H}^q$ is a locally constant presheaf

Rational cohomology ring of complex Grassmannian.

Cobordant 1-manifolds are homologous?

Relation of $\mathbb{Z}_2$-cohomology and interger cohomology

Show a map in cohomology is trivial

Understanding homologies of pairs and induced maps

Filling a hole by eliminating a homology class

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