List questions from homology-cohomology

Published on 14 Apr 2026 - 7:04

420

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Why isn't $H_n(M) \cong 0$ for any $n$-manifold $M$ with non-trivial boundary?

Published on 16 Apr 2026 - 12:35

352

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The first homology and Betti number

Published on 15 Apr 2026 - 0:57

479

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Is this space $S^3$?

Published on 10 May 2026 - 18:19

30

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$\det\partial_2^t∂_2 =m^2 ·k(G)$ with finite connected graph with reduced homology being 0

Published on 16 Apr 2026 - 11:24

122

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Inner circle of torus of revolution is calibrated

Published on 10 May 2026 - 17:00

439

Views

Is there any geometrical intuition for the Hurewicz theorem?

Published on 11 May 2026 - 9:08

723

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De - Rham Cohomology calculation via Mayer - Vietoris Sequences

Published on 11 Apr 2026 - 8:13

424

Views

Group cohomology with coefficients in regular representation

Published on 10 May 2026 - 13:48

222

Views

Working with the homological definition of orientation

Published on 10 May 2026 - 15:02

247

Views

Dimension of homology of $q$-skeleton

Published on 10 May 2026 - 13:26

70

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spectrum theory in generalized cohomology

Published on 13 May 2026 - 3:28

221

Views

For genus $g$ Riemann surface, $\operatorname{H}^1(X)$ has complex dimension $2g$?

Published on 11 May 2026 - 4:37

336

Views

Homology/Cohomology Theories for Non-Locally Connected Spaces

Published on 10 May 2026 - 21:41

849

Views

Connected, compact, orientable smooth manifold with finite fundamental group

Published on 11 Apr 2026 - 18:27

List Question

Degree of map $S^2\times S^2$ to $\mathbb{C}P^2\# \mathbb{C}P^2$

Why isn't $H_n(M) \cong 0$ for any $n$-manifold $M$ with non-trivial boundary?

The first homology and Betti number

Is this space $S^3$?

$\det\partial_2^t∂_2 =m^2 ·k(G)$ with finite connected graph with reduced homology being 0

Inner circle of torus of revolution is calibrated

Is there any geometrical intuition for the Hurewicz theorem?

De - Rham Cohomology calculation via Mayer - Vietoris Sequences

Group cohomology with coefficients in regular representation

Working with the homological definition of orientation

Dimension of homology of $q$-skeleton

spectrum theory in generalized cohomology

For genus $g$ Riemann surface, $\operatorname{H}^1(X)$ has complex dimension $2g$?

Homology/Cohomology Theories for Non-Locally Connected Spaces

Connected, compact, orientable smooth manifold with finite fundamental group

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