List questions from homology-cohomology

Published on 26 May 2018 - 17:39

417

Views

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

Published on 27 May 2018 - 9:40

349

Views

The first homology and Betti number

Published on 27 May 2018 - 18:55

475

Views

Is this space $S^3$?

Published on 25 Mar 2026 - 12:52

27

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

Published on 28 May 2018 - 9:40

121

Views

Inner circle of torus of revolution is calibrated

Published on 25 Mar 2026 - 16:03

436

Views

Is there any geometrical intuition for the Hurewicz theorem?

Published on 25 Mar 2026 - 16:46

720

Views

De - Rham Cohomology calculation via Mayer - Vietoris Sequences

Published on 31 May 2018 - 1:26

421

Views

Group cohomology with coefficients in regular representation

Published on 25 Mar 2026 - 17:19

217

Views

Working with the homological definition of orientation

Published on 25 Mar 2026 - 6:12

242

Views

Dimension of homology of $q$-skeleton

Published on 25 Mar 2026 - 17:20

63

Views

spectrum theory in generalized cohomology

Published on 25 Mar 2026 - 15:38

218

Views

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

Published on 25 Mar 2026 - 7:48

330

Views

Homology/Cohomology Theories for Non-Locally Connected Spaces

Published on 22 Mar 2026 - 22:33

846

Views

Connected, compact, orientable smooth manifold with finite fundamental group

Published on 03 Jun 2018 - 1:20

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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