List questions from exact-sequence

Published on 30 Jan 2021 - 1:32

91

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$\lim_{n\to\infty}\sqrt[3]{3n}\sigma_n=1$

Published on 02 Feb 2021 - 19:28

209

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Short Exact Sequence of a Hyperplane in the Projective Space

Published on 28 Mar 2026 - 10:15

115

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Does the short exact sequence $0\mapsto \mathbb{Z}^k\mapsto \Gamma\mapsto \mathbb{Z}^\ell\mapsto 0$ split?

Published on 05 Feb 2021 - 5:01

343

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What are the implications of a surjection between free modules?

Published on 29 Mar 2026 - 15:03

62

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Is an exact-by-nuclear extension of $C^*$-algebras again exact?

Published on 08 Feb 2021 - 14:27

72

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How do I understand the ratios between $\pi_1(U(N))=\mathbb{Z}$, $\pi_1(U(1))=\mathbb{Z}$, and $\pi_1(PSU(N))=\mathbb{Z}/N$?

Published on 14 Feb 2021 - 19:08

534

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Long exact sequence for mapping torus from Mayer-Vietoris

Published on 16 Feb 2021 - 12:06

946

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Künneth formula for cohomology

Published on 18 Feb 2021 - 13:37

223

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Direct proof that a short exact sequence induces a quasi-isomorphism from the mapping cone

Published on 23 Feb 2021 - 18:45

42

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Exact short sequence

Published on 24 Feb 2021 - 14:55

114

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Proof of the exact sequence $0\to H^i(M)\to \operatorname{coker} d^{i-1}\to\ker d^{i+1}\to H^{i+1}(M)\to 0$.

Published on 25 Feb 2021 - 10:07

138

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Linear algebra vs homological algebra

Published on 25 Feb 2021 - 12:52

162

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If $G_1, G_2, G_3$ are abelian groups and $0 \to G_1 \to G_2 \to G_3 \to 0$ is exact, then $G_2 \simeq G_1 \oplus G_3$

Published on 25 Feb 2021 - 13:02

317

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About the functoriality of the long exact sequence in cohomology

Published on 26 Feb 2021 - 12:19

List Question

Tensor with an Exact Sequence of Free Module Still Exact?

$\lim_{n\to\infty}\sqrt[3]{3n}\sigma_n=1$

Short Exact Sequence of a Hyperplane in the Projective Space

Does the short exact sequence $0\mapsto \mathbb{Z}^k\mapsto \Gamma\mapsto \mathbb{Z}^\ell\mapsto 0$ split?

What are the implications of a surjection between free modules?

Is an exact-by-nuclear extension of $C^*$-algebras again exact?

How do I understand the ratios between $\pi_1(U(N))=\mathbb{Z}$, $\pi_1(U(1))=\mathbb{Z}$, and $\pi_1(PSU(N))=\mathbb{Z}/N$?

Long exact sequence for mapping torus from Mayer-Vietoris

Künneth formula for cohomology

Direct proof that a short exact sequence induces a quasi-isomorphism from the mapping cone

Exact short sequence

Proof of the exact sequence $0\to H^i(M)\to \operatorname{coker} d^{i-1}\to\ker d^{i+1}\to H^{i+1}(M)\to 0$.

Linear algebra vs homological algebra

If $G_1, G_2, G_3$ are abelian groups and $0 \to G_1 \to G_2 \to G_3 \to 0$ is exact, then $G_2 \simeq G_1 \oplus G_3$

About the functoriality of the long exact sequence in cohomology

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