List questions from homology-cohomology

Published on 30 Mar 2026 - 14:10

2k

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If $M$ is a compact, contractible $n$-manifold (with boundary) then $\partial M$ is a homology (n-1)-sphere.

Published on 05 Oct 2018 - 23:21

242

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Closed oriented even dimensional manifold with only three non-zero Betti numbers.

Published on 22 Mar 2026 - 12:52

276

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Closed oriented manifold with middle Betti is one with odd degree.

Published on 22 Mar 2026 - 21:46

907

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What is the cellular homology of a CW complex $X$ from long exact sequence of relative homology?

Published on 25 Mar 2026 - 6:13

320

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What's the ring structure of $H^*(C_2,\mathbb{Z})$ with a nontrivial group action?

Published on 25 Mar 2026 - 20:27

177

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Direct proof for Cech Cohomology stabilizing for a good open cover

Published on 30 Mar 2026 - 16:10

1.2k

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Finitely Generated Homology Groups

Published on 13 Oct 2018 - 19:19

2.6k

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Definition of graded abelian group

Published on 30 Mar 2026 - 16:05

57

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How to calculate $H_n(\ast)$?

Published on 15 Oct 2018 - 4:34

524

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Homology change by removing a simplex and its face

Published on 15 Oct 2018 - 17:16

280

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Betti number of the cut torus

Published on 15 Oct 2018 - 20:24

1.8k

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Homotopic maps induce the same homomorphism for reduced homology groups

Published on 16 Oct 2018 - 9:37

979

Views

Künneth Theorem For Product of Projective Spaces

Published on 16 Oct 2018 - 21:37

225

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Proof verification: the homology groups of the cube.

Published on 16 Oct 2018 - 23:09

List Question

category of sheaves of abelian groups properties

If $M$ is a compact, contractible $n$-manifold (with boundary) then $\partial M$ is a homology (n-1)-sphere.

Closed oriented even dimensional manifold with only three non-zero Betti numbers.

Closed oriented manifold with middle Betti is one with odd degree.

What is the cellular homology of a CW complex $X$ from long exact sequence of relative homology?

What's the ring structure of $H^*(C_2,\mathbb{Z})$ with a nontrivial group action?

Direct proof for Cech Cohomology stabilizing for a good open cover

Finitely Generated Homology Groups

Definition of graded abelian group

How to calculate $H_n(\ast)$?

Homology change by removing a simplex and its face

Betti number of the cut torus

Homotopic maps induce the same homomorphism for reduced homology groups

Künneth Theorem For Product of Projective Spaces

Proof verification: the homology groups of the cube.

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