Question

Isomorphism between torsion subgroups of $H_q (M)$ and $H_{n-q-1} (M)$ where $M$ is a compact oriented $n$-manifold

score 363 · Answer 1 · 2026-03-31 10:57:22

363

Views

Isomorphism between torsion subgroups of $H_q (M)$ and $H_{n-q-1} (M)$ where $M$ is a compact oriented $n$-manifold

Published on 31 Mar 2026 - 10:57

score 539 · Answer 2 · 2019-01-03 14:22:40

539

Views

Changing coefficients of cohomology and pullbacks

Published on 03 Jan 2019 - 14:22

score 200 · Answer 3 · 2026-03-26 17:42:27

200

Views

Using simplicial homology to compute topological spaces homeomorphic to the quotient spaces of polygons

Published on 26 Mar 2026 - 17:42

score 116 · Answer 4 · 2019-01-05 19:18:14

116

Views

Removing Homology Groups

Published on 05 Jan 2019 - 19:18

score 28 · Answer 5 · 2026-03-31 10:47:54

28

Views

For a group homomorphism $\alpha : G\rightarrow G'$, does the pullback $\alpha^\# : Mod(G')\rightarrow Mod(G)$ send $G'$-projectives to $G$-acyclics?

Published on 31 Mar 2026 - 10:47

score 319 · Answer 6 · 2026-03-26 01:25:15

319

Views

cohomological dimension of groups vs cohomological dimension of subgroups

Published on 26 Mar 2026 - 1:25

score 201 · Answer 7 · 2019-01-07 09:05:59

201

Views

Wedge axiom of a homology theory like functor

Published on 07 Jan 2019 - 9:05

score 24 · Answer 8 · 2026-03-26 12:06:41

24

Views

How do you call groups formed as direct sums of cyclic groups?

Published on 26 Mar 2026 - 12:06

score 58 · Answer 9 · 2019-01-07 16:48:04

58

Views

Is repeating a loop twice the same as multiplication by $2$ in singular homology?

Published on 07 Jan 2019 - 16:48

score 89 · Answer 10 · 2019-01-08 16:47:24

89

Views

Lusternik-Schnirelmann category of $\mathbb{RP}^2 = 3$ (or $2$ depending on the definition) using only homology

Published on 08 Jan 2019 - 16:47

score 357 · Answer 11 · 2019-01-10 07:21:00

357

Views

On topological space whose homology groups/modules are trivial

Published on 10 Jan 2019 - 7:21

score 75 · Answer 12 · 2019-01-10 08:17:49

75

Views

Connected Hausdorff space all whose $n$-th homology groups, for $n\ge 1$, are trivial

Published on 10 Jan 2019 - 8:17

score 45 · Answer 13 · 2026-03-26 10:45:12

45

Views

Is there an algorithmic way to compute the quotient of two subgroups of $\mathbb Z^n$?

Published on 26 Mar 2026 - 10:45

score 79 · Answer 14 · 2026-03-26 14:22:13

79

Views

The ampleness of canonical sheaves and the proof of "$X \simeq \mathrm{Proj}\left(\bigoplus_k H^0(X, \omega_X^k)\right)$".

Published on 26 Mar 2026 - 14:22

score 36 · Answer 15 · 2026-03-25 12:54:40

36

Views

Ring isomorphism between $H^*(G_n(\Bbb F^\infty); R)$ and Ring of characteristic classes

Published on 25 Mar 2026 - 12:54

List Question

Isomorphism between torsion subgroups of $H_q (M)$ and $H_{n-q-1} (M)$ where $M$ is a compact oriented $n$-manifold

Changing coefficients of cohomology and pullbacks

Using simplicial homology to compute topological spaces homeomorphic to the quotient spaces of polygons

Removing Homology Groups

For a group homomorphism $\alpha : G\rightarrow G'$, does the pullback $\alpha^\# : Mod(G')\rightarrow Mod(G)$ send $G'$-projectives to $G$-acyclics?

cohomological dimension of groups vs cohomological dimension of subgroups

Wedge axiom of a homology theory like functor

How do you call groups formed as direct sums of cyclic groups?

Is repeating a loop twice the same as multiplication by $2$ in singular homology?

Lusternik-Schnirelmann category of $\mathbb{RP}^2 = 3$ (or $2$ depending on the definition) using only homology

On topological space whose homology groups/modules are trivial

Connected Hausdorff space all whose $n$-th homology groups, for $n\ge 1$, are trivial

Is there an algorithmic way to compute the quotient of two subgroups of $\mathbb Z^n$?

The ampleness of canonical sheaves and the proof of "$X \simeq \mathrm{Proj}\left(\bigoplus_k H^0(X, \omega_X^k)\right)$".

Ring isomorphism between $H^*(G_n(\Bbb F^\infty); R)$ and Ring of characteristic classes

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