List questions from homology-cohomology

Published on 25 Mar 2026 - 23:39

767

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Homology group of $X=\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$

Published on 29 Mar 2026 - 18:36

1.1k

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Chain complex homotopy equivalent to its homology

Published on 31 Mar 2026 - 13:10

697

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Homology of the $n$-sphere

Published on 17 Jan 2019 - 20:17

321

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Borel subgroup of $SL_2(\mathbb{Z})$

Published on 26 Mar 2026 - 1:03

664

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Existence of sphere maps of arbitrary degree

Published on 17 Jan 2019 - 23:26

49

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A natural isomomorphism of $G$-modules

Published on 30 Mar 2026 - 15:13

104

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How to get the cohomology group in the exact sequence? $B_n^* \leftarrow Z_n^* \leftarrow H^n(C;G) \leftarrow B_{n-1}^* \leftarrow Z_{n-1}^*$

Published on 20 Jan 2019 - 6:46

300

Views

Help with homology axioms

Published on 21 Jan 2019 - 12:49

132

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Certain Galois cohomology computation

Published on 26 Mar 2026 - 16:06

106

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Homology groups of the set with Mayer-Veitoris

Published on 31 Mar 2026 - 13:14

156

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Can you express this easy theorem in fancy categorical terms?

Published on 23 Jan 2019 - 13:26

169

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Exercise in Simplicial Homology

Published on 23 Jan 2019 - 16:04

268

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A kind of horseshoe lemma on the injective resolution

Published on 25 Mar 2026 - 9:27

47

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about the cohomology of a tensor module.

Published on 31 Mar 2026 - 15:17

List Question

Misunderstanding in definition of homology of groups

Homology group of $X=\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$

Chain complex homotopy equivalent to its homology

Homology of the $n$-sphere

Borel subgroup of $SL_2(\mathbb{Z})$

Existence of sphere maps of arbitrary degree

A natural isomomorphism of $G$-modules

How to get the cohomology group in the exact sequence? $B_n^* \leftarrow Z_n^* \leftarrow H^n(C;G) \leftarrow B_{n-1}^* \leftarrow Z_{n-1}^*$

Help with homology axioms

Certain Galois cohomology computation

Homology groups of the set with Mayer-Veitoris

Can you express this easy theorem in fancy categorical terms?

Exercise in Simplicial Homology

A kind of horseshoe lemma on the injective resolution

about the cohomology of a tensor module.

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