Question

Calculate the map on homology induced by the quotient map $S^ 3 → \Bbb R {\Bbb P}^3$

score 787 · Answer 1 · 2019-04-17 14:33:29

Calculate the map on homology induced by the quotient map $S^ 3 → \Bbb R {\Bbb P}^3$

Published on 17 Apr 2019 - 14:33

score 75 · Answer 2 · 2026-03-25 22:06:29

Hint wanted: Any order-preserving $\phi:[m] \to [n]$ can be decomposed uniquely as composition of an injective and a surjective function

score 167 · Answer 3 · 2019-04-17 16:09:45

167

Views

Any map from $X \to {(S^1 )}^k$ induces a 0 map on reduced homology.

Published on 17 Apr 2019 - 16:09

score 394 · Answer 4 · 2019-04-17 16:38:47

394

Views

Prove that any map $T → T$ ($T$ = Torus) whose restriction to $S^1 ∨ S^1$ is null-homotopic induces a $0$ map on reduced homology

Published on 17 Apr 2019 - 16:38

score 80 · Answer 5 · 2026-04-01 04:30:41

80

Views

Prove that there is a long exact sequence $\ldots → H_k(X) \overset{2}\to H_k(X) → H_k(X;\Bbb Z/2) → H_ {k−1} (X) → · · ·$

Published on 01 Apr 2026 - 4:30

score 337 · Answer 6 · 2019-04-17 21:20:43

337

Views

Compute the effect of $∆_∗$ on homology groups.

Published on 17 Apr 2019 - 21:20

score 472 · Answer 7 · 2026-03-30 15:29:22

472

Views

Dualizing from co-invariants to invariants

Published on 30 Mar 2026 - 15:29

score 197 · Answer 8 · 2026-03-25 13:04:52

197

Views

Serre Spectral Sequence I

Published on 25 Mar 2026 - 13:04

score 101 · Answer 9 · 2026-03-26 09:42:38

101

Views

Existence of a countable locally finite cover with nonempty intersection of two adjacent elements

Published on 26 Mar 2026 - 9:42

score 282 · Answer 10 · 2019-04-20 15:43:12

282

Views

Inclusion of $n$-skeleton induces surjection of cohomology rings

Published on 20 Apr 2019 - 15:43

score 317 · Answer 11 · 2019-04-21 13:06:42

317

Views

Associativity of a homology ring of an H-space.

Published on 21 Apr 2019 - 13:06

score 2.2k · Answer 12 · 2026-03-25 19:01:34

2.2k

Views

What is Thom Isomorphism?

Published on 25 Mar 2026 - 19:01

score 101 · Answer 13 · 2026-04-01 04:28:13

101

Views

Question on why a particular quasi-isomorphism between complexes doens't have an inverse

Published on 01 Apr 2026 - 4:28

score 233 · Answer 14 · 2019-04-24 13:00:45

233

Views

Problems understanding 0th relative cohomology

Published on 24 Apr 2019 - 13:00

score 21 · Answer 15 · 2019-04-24 13:02:56

21

Views

n-singular chains are result of a group action?

Published on 24 Apr 2019 - 13:02

List Question

Calculate the map on homology induced by the quotient map $S^ 3 → \Bbb R {\Bbb P}^3$

Hint wanted: Any order-preserving $\phi:[m] \to [n]$ can be decomposed uniquely as composition of an injective and a surjective function

Any map from $X \to {(S^1 )}^k$ induces a 0 map on reduced homology.

Prove that any map $T → T$ ($T$ = Torus) whose restriction to $S^1 ∨ S^1$ is null-homotopic induces a $0$ map on reduced homology

Prove that there is a long exact sequence $\ldots → H_k(X) \overset{2}\to H_k(X) → H_k(X;\Bbb Z/2) → H_ {k−1} (X) → · · ·$

Compute the effect of $∆_∗$ on homology groups.

Dualizing from co-invariants to invariants

Serre Spectral Sequence I

Existence of a countable locally finite cover with nonempty intersection of two adjacent elements

Inclusion of $n$-skeleton induces surjection of cohomology rings

Associativity of a homology ring of an H-space.

What is Thom Isomorphism?

Question on why a particular quasi-isomorphism between complexes doens't have an inverse

Problems understanding 0th relative cohomology

n-singular chains are result of a group action?

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