List questions from homology-cohomology

Published on 25 Mar 2026 - 9:36

425

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Homotopy invariance of singular cohomology groups

Published on 02 Apr 2026 - 3:50

158

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Natural classes in cohomology ring of symmetric product of curves

Published on 26 Mar 2026 - 12:08

1.1k

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Singular homology of a torus

Published on 17 Sep 2019 - 8:03

274

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Number of connected components of a preimage

Published on 01 Apr 2026 - 7:58

245

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Singular cohomology of complex projective space

Published on 25 Mar 2026 - 5:06

44

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Homeomorphism of $\vert K\vert_d$ and $S^1$

Published on 26 Mar 2026 - 0:53

346

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Why $H^p(\coprod_{i\in I}X_i;G)\cong \prod_{i\in I}H^p(X_i;G)$?

Published on 02 Apr 2026 - 5:35

423

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On 2-cocycles defined on direct product

Published on 20 Sep 2019 - 14:17

29

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Canonical isomorphism between $H_0(X, A)$ and $A$ for $X$ a topological space.

Published on 21 Sep 2019 - 17:43

850

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Basic obstruction theory : where does the obstruction to uniqueness of lifting lie?

Published on 22 Mar 2026 - 22:53

353

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(elementary?) proof of simplicial homology groups of $\Delta_n$

Published on 26 Mar 2026 - 0:53

46

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Can we also define $R^iF(i=0,1,\cdots)$?

Published on 23 Sep 2019 - 11:36

126

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No quasi-isomorphism

Published on 25 Mar 2026 - 18:04

227

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Free resolution of a group $G$ and the chain complex of the universal cover of $K(G,1)$

Published on 25 Mar 2026 - 14:25

List Question

Unstable manifold of height function on torus

Homotopy invariance of singular cohomology groups

Natural classes in cohomology ring of symmetric product of curves

Singular homology of a torus

Number of connected components of a preimage

Singular cohomology of complex projective space

Homeomorphism of $\vert K\vert_d$ and $S^1$

Why $H^p(\coprod_{i\in I}X_i;G)\cong \prod_{i\in I}H^p(X_i;G)$?

On 2-cocycles defined on direct product

Canonical isomorphism between $H_0(X, A)$ and $A$ for $X$ a topological space.

Basic obstruction theory : where does the obstruction to uniqueness of lifting lie?

(elementary?) proof of simplicial homology groups of $\Delta_n$

Can we also define $R^iF(i=0,1,\cdots)$?

No quasi-isomorphism

Free resolution of a group $G$ and the chain complex of the universal cover of $K(G,1)$

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