Question

Motivation for the relations defining $H^1(G,A)$ for non-commutative cohomology

score 646 · Answer 1 · 2026-03-26 16:06:25

646

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Motivation for the relations defining $H^1(G,A)$ for non-commutative cohomology

Published on 26 Mar 2026 - 16:06

score 317 · Answer 2 · 2013-01-24 14:23:23

317

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Group extension: $H^n(\mathbb{Z},M)$

Published on 24 Jan 2013 - 14:23

score 1k · Answer 3 · 2013-02-04 15:05:33

1k

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Does $f(gh)=gf(h)+f(g)$ make $H^1(G,A)$ small enough?

Published on 04 Feb 2013 - 15:05

score 6.9k · Answer 4 · 2013-02-24 02:16:06

6.9k

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What is the intuition between 1-cocycles (group cohomology)?

Published on 24 Feb 2013 - 2:16

score 88 · Answer 5 · 2013-02-25 00:26:32

88

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Are these maps group homomorphisms?

Published on 25 Feb 2013 - 0:26

score 149 · Answer 6 · 2020-08-05 00:13:22

149

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Fundamental Group of Klein Bottle acts on $\mathbb{R}$

Published on 05 Aug 2020 - 0:13

score 467 · Answer 7 · 2026-03-27 18:49:35

467

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Why there is no suspension axiom for homology ? and why there is no excision axiom for cohomology theory?

Published on 27 Mar 2026 - 18:49

score 87 · Answer 8 · 2020-08-07 01:15:05

87

Views

Chain complex and cohomology

Published on 07 Aug 2020 - 1:15

score 49 · Answer 9 · 2026-03-27 22:15:05

49

Views

Pairing Cohomology with Homology on pg.510 in "Modern classical homotopy theory".

Published on 27 Mar 2026 - 22:15

score 38 · Answer 10 · 2020-08-07 11:22:15

38

Views

The group of cohomology $H^3(G,\mathbb{Z})$ is finite when $G$ is finite.

Published on 07 Aug 2020 - 11:22

score 39 · Answer 11 · 2020-08-08 14:57:05

39

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each $u\in (\mathbb{Z}G\otimes_\mathbb{Z}A)^S$ has a unique expression $\Sigma_x{_\in}{_G}n_xx$

Published on 08 Aug 2020 - 14:57

score 32 · Answer 12 · 2020-08-09 09:48:02

32

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an isomorphism: $H^{q-1}(G,C) \xrightarrow{\delta} H^q(G,A)$.

Published on 09 Aug 2020 - 9:48

score 269 · Answer 13 · 2026-03-27 13:03:22

269

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Understanding the proof on why the first cohomology group of a Galois extension is trivial

Published on 27 Mar 2026 - 13:03

score 26 · Answer 14 · 2020-08-11 05:17:47

26

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H$^1 (G,\mathbb{Z}) \cong$ Der$(G, \mathbb{Z})$/PDer $(G, \mathbb{Z})\cong$ Hom$(\mathbb{Z}, \mathbb{Z}) \neq {0}$.

Published on 11 Aug 2020 - 5:17

score 162 · Answer 15 · 2026-03-25 15:12:10

162

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Kummer Theory: Understanding the isomorphism $F^\times \cap E^{\times n}/F^{\times n} \to \operatorname{Hom}(G,\mu_n)$

Published on 25 Mar 2026 - 15:12

List Question

Motivation for the relations defining $H^1(G,A)$ for non-commutative cohomology

Group extension: $H^n(\mathbb{Z},M)$

Does $f(gh)=gf(h)+f(g)$ make $H^1(G,A)$ small enough?

What is the intuition between 1-cocycles (group cohomology)?

Are these maps group homomorphisms?

Fundamental Group of Klein Bottle acts on $\mathbb{R}$

Why there is no suspension axiom for homology ? and why there is no excision axiom for cohomology theory?

Chain complex and cohomology

Pairing Cohomology with Homology on pg.510 in "Modern classical homotopy theory".

The group of cohomology $H^3(G,\mathbb{Z})$ is finite when $G$ is finite.

each $u\in (\mathbb{Z}G\otimes_\mathbb{Z}A)^S$ has a unique expression $\Sigma_x{_\in}{_G}n_xx$

an isomorphism: $H^{q-1}(G,C) \xrightarrow{\delta} H^q(G,A)$.

Understanding the proof on why the first cohomology group of a Galois extension is trivial

H$^1 (G,\mathbb{Z}) \cong$ Der$(G, \mathbb{Z})$/PDer $(G, \mathbb{Z})\cong$ Hom$(\mathbb{Z}, \mathbb{Z}) \neq {0}$.

Kummer Theory: Understanding the isomorphism $F^\times \cap E^{\times n}/F^{\times n} \to \operatorname{Hom}(G,\mu_n)$

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