Question

Any embedding $\mathbb{R} P^n\hookrightarrow \mathbb{R} P^{\infty}$ induces a surjection of the singular cohomology rings.

score 87 · Answer 1 · 2026-03-26 22:16:06

87

Views

Any embedding $\mathbb{R} P^n\hookrightarrow \mathbb{R} P^{\infty}$ induces a surjection of the singular cohomology rings.

Published on 26 Mar 2026 - 22:16

score 273 · Answer 2 · 2019-08-11 10:57:43

273

Views

To Understand The Cohomology ring $H^*(\mathbb{R}P^n;\mathbb{Z})$

Published on 11 Aug 2019 - 10:57

score 100 · Answer 3 · 2019-08-12 00:51:10

100

Views

Prove that $f_*: H_2(T; \mathbb{Z}/2)\to H_2(K; \mathbb{Z}/2)$ is the trivial mapping.

Published on 12 Aug 2019 - 0:51

score 53 · Answer 4 · 2019-08-12 08:01:47

53

Views

Why does the relative homology group vanish modulo the set of proper faces

Published on 12 Aug 2019 - 8:01

score 172 · Answer 5 · 2026-03-25 13:33:26

172

Views

GAP — compute kernel of a matrix with coefficients in a finite ring

Published on 25 Mar 2026 - 13:33

score 123 · Answer 6 · 2019-08-13 17:05:14

123

Views

How to compute cohomology of $C^0(S^n,X)$?

Published on 13 Aug 2019 - 17:05

score 244 · Answer 7 · 2019-08-14 10:35:03

244

Views

Some Homology and Cohomology Calculations for the quotient map $q:S^n\rightarrow \mathbb{R}P^n$

Published on 14 Aug 2019 - 10:35

score 395 · Answer 8 · 2019-08-14 15:21:12

395

Views

A function $f:X \to Y$ which induces isomorphisms on all homology groups but $X$ and $Y$ have non-isomorphic cohomology rings.

Published on 14 Aug 2019 - 15:21

score 239 · Answer 9 · 2026-03-25 15:58:58

239

Views

Definition of equivariant chain complex.

Published on 25 Mar 2026 - 15:58

score 147 · Answer 10 · 2026-03-26 09:48:13

147

Views

free group acting on the 3D sphere

Published on 26 Mar 2026 - 9:48

score 32 · Answer 11 · 2019-08-16 05:35:36

Need a description of the map $i:\mathbb{C}P^2\vee\mathbb{C}P^2\rightarrow \mathbb{C}P^2\times \mathbb{C}P^2$ on $2$nd Cohomology level

score 46 · Answer 12 · 2026-03-28 02:04:33

46

Views

How do you do simplicial homology with $0, 1$ coefficients?

Published on 28 Mar 2026 - 2:04

score 57 · Answer 13 · 2026-02-23 01:08:07

57

Views

A compact convex set $A$ is contained in $\mathbb{R}^n$ then for any section $x \rightarrow a_x$ there is a unique $a_A \rightarrow a_x$

Published on 23 Feb 2026 - 1:08

score 43 · Answer 14 · 2026-04-01 22:39:11

43

Views

$h_:S_(X\times Y)\to S_(X\times Y)$ a homomorphism of natural chain complexes. If $h_0=Id$, show that $h_$ is homotopic to $Id$

Published on 01 Apr 2026 - 22:39

score 562 · Answer 15 · 2026-04-02 00:24:06

562

Views

Show that $\operatorname{Tor}(A, B)$ is always a torsion group

Published on 02 Apr 2026 - 0:24

List Question

Any embedding $\mathbb{R} P^n\hookrightarrow \mathbb{R} P^{\infty}$ induces a surjection of the singular cohomology rings.

To Understand The Cohomology ring $H^*(\mathbb{R}P^n;\mathbb{Z})$

Prove that $f_*: H_2(T; \mathbb{Z}/2)\to H_2(K; \mathbb{Z}/2)$ is the trivial mapping.

Why does the relative homology group vanish modulo the set of proper faces

GAP — compute kernel of a matrix with coefficients in a finite ring

How to compute cohomology of $C^0(S^n,X)$?

Some Homology and Cohomology Calculations for the quotient map $q:S^n\rightarrow \mathbb{R}P^n$

A function $f:X \to Y$ which induces isomorphisms on all homology groups but $X$ and $Y$ have non-isomorphic cohomology rings.

Definition of equivariant chain complex.

free group acting on the 3D sphere

Need a description of the map $i:\mathbb{C}P^2\vee\mathbb{C}P^2\rightarrow \mathbb{C}P^2\times \mathbb{C}P^2$ on $2$nd Cohomology level

How do you do simplicial homology with $0, 1$ coefficients?

A compact convex set $A$ is contained in $\mathbb{R}^n$ then for any section $x \rightarrow a_x$ there is a unique $a_A \rightarrow a_x$

$h_:S_(X\times Y)\to S_(X\times Y)$ a homomorphism of natural chain complexes. If $h_0=Id$, show that $h_$ is homotopic to $Id$

Show that $\operatorname{Tor}(A, B)$ is always a torsion group

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