List questions from homology-cohomology

Published on 27 Mar 2026 - 4:34

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Cohomology of free groups topologically

Published on 25 Mar 2026 - 19:05

309

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Homology of infinite dimensional real projective space given by Tor-functor

Published on 31 Mar 2026 - 15:18

83

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Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

Published on 25 Mar 2026 - 4:42

163

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is Euler characteristic with coefficients in local system equal usual Euler characteristic times rank, for non-compact spaces?

Published on 01 Feb 2019 - 17:23

124

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Does trivial cohomology of spectra imply trivial homology?

Published on 25 Mar 2026 - 8:30

98

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$m>n$, $f: \mathbb{RP}^m \to \mathbb{RP}^n$ continuous map. Prove that $f_{*}$ is zero map in reduced homology.

Published on 03 Feb 2019 - 18:46

244

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Simplicial and De Rham Homology on Manifolds

Published on 25 Mar 2026 - 20:13

66

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Why does $Ext_{R}^{n}(I,B)\neq 0$, $I$ is injective with $pd(I)=n$, & $B$ the image of a projective $P$, imply $Ext_{R}^{n}(I,P)\neq 0$?

Published on 31 Mar 2026 - 17:01

358

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Group homomorphism induces cohomology homomorphism

Published on 25 Mar 2026 - 6:05

1k

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Hatcher Exercise 3.2.9

Published on 26 Mar 2026 - 12:51

177

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Self intersection and cohomology of boundary of tubular neighbourhood

Published on 26 Mar 2026 - 6:01

155

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Definitions of Group Cohomology

Published on 26 Mar 2026 - 1:10

495

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Is there a Mayer-Vietoris sequence for an (uncountably) infinite collection of sets?

Published on 25 Mar 2026 - 22:26

3.7k

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Why is this called the cocycle condition?

Published on 25 Mar 2026 - 10:59

List Question

Projective resolution of short exact sequence: definition in Jacobson

Cohomology of free groups topologically

Homology of infinite dimensional real projective space given by Tor-functor

Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

is Euler characteristic with coefficients in local system equal usual Euler characteristic times rank, for non-compact spaces?

Does trivial cohomology of spectra imply trivial homology?

$m>n$, $f: \mathbb{RP}^m \to \mathbb{RP}^n$ continuous map. Prove that $f_{*}$ is zero map in reduced homology.

Simplicial and De Rham Homology on Manifolds

Why does $Ext_{R}^{n}(I,B)\neq 0$, $I$ is injective with $pd(I)=n$, & $B$ the image of a projective $P$, imply $Ext_{R}^{n}(I,P)\neq 0$?

Group homomorphism induces cohomology homomorphism

Hatcher Exercise 3.2.9

Self intersection and cohomology of boundary of tubular neighbourhood

Definitions of Group Cohomology

Is there a Mayer-Vietoris sequence for an (uncountably) infinite collection of sets?

Why is this called the cocycle condition?

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