List questions from homology-cohomology

Published on 26 Mar 2026 - 23:23

323

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Computing the homology of $\mathbb{S}^1$ attached with two $2$-cells via degree $2$ and $3$

Published on 25 Mar 2026 - 6:04

87

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Homology union three subspaces.

Published on 25 Mar 2026 - 7:15

355

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How are rational algebraic Hodge classes of type $ (p,p) $ defined?

Published on 22 Mar 2026 - 5:22

72

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Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$

Published on 20 Mar 2026 - 13:30

1.5k

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Chern classes, cohomology classes with real/integer coefficients

Published on 22 Mar 2026 - 13:39

193

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Cohomology groups $H^p(K;Z)$ where $K$ is finite simplicial complex are finitely generated abelian groups

Published on 25 Mar 2026 - 10:35

341

Views

Is there any intuition for finding cohomology groups of famous manifolds?

Published on 25 Mar 2026 - 10:35

362

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Orientation class in relative homology and integration

Published on 25 Mar 2026 - 11:53

64

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Given $f:X\to Y$, what relation between induced maps $H_k(X) \to H_k(Y)$ and $H^k(Y) \to H^k(X)$?

Published on 25 Mar 2026 - 13:34

290

Views

What is the pushout of $D^n \longleftarrow S^{n-1} \longrightarrow D^n$?

Published on 26 Mar 2026 - 5:36

105

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Group theoretic interpretation of the cohomology of $K(G, n)$

Published on 22 Mar 2026 - 2:54

173

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why is this figure not a simplicial complex?

Published on 25 Mar 2026 - 15:21

168

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Induced maps in local homology and isotopies

Published on 25 Mar 2026 - 11:15

269

Views

Crossed homomorphism/derivation on free group

Published on 28 Mar 2026 - 17:22

List Question

Injective objects in a category

Computing the homology of $\mathbb{S}^1$ attached with two $2$-cells via degree $2$ and $3$

Homology union three subspaces.

How are rational algebraic Hodge classes of type $ (p,p) $ defined?

Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$

Chern classes, cohomology classes with real/integer coefficients

Cohomology groups $H^p(K;Z)$ where $K$ is finite simplicial complex are finitely generated abelian groups

Is there any intuition for finding cohomology groups of famous manifolds?

Orientation class in relative homology and integration

Given $f:X\to Y$, what relation between induced maps $H_k(X) \to H_k(Y)$ and $H^k(Y) \to H^k(X)$?

What is the pushout of $D^n \longleftarrow S^{n-1} \longrightarrow D^n$?

Group theoretic interpretation of the cohomology of $K(G, n)$

why is this figure not a simplicial complex?

Induced maps in local homology and isotopies

Crossed homomorphism/derivation on free group

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