List questions from homology-cohomology

Published on 11 Apr 2026 - 17:38

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Lens space and its generalization, homotopy/homology groups

Published on 13 Apr 2026 - 8:27

308

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The homology class associated to a hypersurface?

Published on 12 Apr 2026 - 14:58

2k

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What's the intuitive, geometric meaning of torsion in homology groups

Published on 12 Apr 2026 - 5:28

426

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Map induced in homology by inclusion

Published on 10 May 2026 - 15:45

32

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Apparent contradiction in computing $H^{0}(M,\mathbb{Z}_{2})$ for a compact manifold with boundary.

Published on 11 Apr 2026 - 19:18

61

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A cycle $A$ homologous to another cycle $B$ is well disjoint with $B$?

Published on 12 Apr 2026 - 5:14

62

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two versions of the Euler class

Published on 10 May 2026 - 12:51

40

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A result for $S^n$ using singular homology, from Vick's book.

Published on 12 Apr 2026 - 18:36

50

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Comparing the cohomology rings of two central extensions

Published on 14 May 2026 - 20:48

113

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Understanding a part of the proof of the Invariance of domain from Hatcher

Published on 14 May 2026 - 22:29

159

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Proving homology class of a loop to be zero

Published on 11 Apr 2026 - 0:13

44

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Explicit isomorphism $H_n(\Delta^n, \partial \Delta^n) \cong \mathbb{Z}$

Published on 10 Apr 2026 - 15:53

89

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Why is the primitive cohomology real?

Published on 10 May 2026 - 16:32

1k

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Boundary operator of $n$-chain composed with itself is zero

Published on 10 Apr 2026 - 7:37

List Question

Injection on homology dual to surjection on cohomology?

Lens space and its generalization, homotopy/homology groups

The homology class associated to a hypersurface?

What's the intuitive, geometric meaning of torsion in homology groups

Map induced in homology by inclusion

Apparent contradiction in computing $H^{0}(M,\mathbb{Z}_{2})$ for a compact manifold with boundary.

A cycle $A$ homologous to another cycle $B$ is well disjoint with $B$?

two versions of the Euler class

A result for $S^n$ using singular homology, from Vick's book.

Comparing the cohomology rings of two central extensions

Understanding a part of the proof of the Invariance of domain from Hatcher

Proving homology class of a loop to be zero

Explicit isomorphism $H_n(\Delta^n, \partial \Delta^n) \cong \mathbb{Z}$

Why is the primitive cohomology real?

Boundary operator of $n$-chain composed with itself is zero

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