Question

Show that any continuous map $f: \mathbb{R}^n \rightarrow X$ is homotopic to the constant map

score 155 · Answer 1 · 2026-04-14 16:53:11

155

Views

Show that any continuous map $f: \mathbb{R}^n \rightarrow X$ is homotopic to the constant map

Published on 14 Apr 2026 - 16:53

score 168 · Answer 2 · 2026-04-13 15:03:31

168

Views

Connected one-dimensional CW complex and homotopy groups

Published on 13 Apr 2026 - 15:03

score 55 · Answer 3 · 2026-04-10 08:42:34

55

Views

Homology isomorphism between H-spaces

Published on 10 Apr 2026 - 8:42

score 102 · Answer 4 · 2026-04-14 08:41:14

102

Views

Split cofiber sequence

Published on 14 Apr 2026 - 8:41

score 53 · Answer 5 · 2026-03-26 01:29:08

53

Views

Let $X$ and $Y$ are copies of $S^2$ taking points $x_1,x_2 \in X$ and $y_1, y_2 \in Y$ then $\pi_1(X \bigsqcup Y/x_1\sim y_1,y_2\sim x_2 )?$

Published on 26 Mar 2026 - 1:29

score 86 · Answer 6 · 2026-04-11 09:51:35

86

Views

Homotopy fiber of a bundle

Published on 11 Apr 2026 - 9:51

score 111 · Answer 7 · 2026-04-08 22:33:46

111

Views

Killing Homology classes in 'controlled' way à la in Postnikov tower

Published on 08 Apr 2026 - 22:33

score 140 · Answer 8 · 2026-03-25 04:40:41

140

Views

Modification of a CW-Complex $X$ with control over Homology groups

Published on 25 Mar 2026 - 4:40

score 62 · Answer 9 · 2026-04-11 16:13:45

62

Views

Which homotopy colimits commute with finite homotopy limits?

Published on 11 Apr 2026 - 16:13

score 127 · Answer 10 · 2026-03-25 12:38:55

127

Views

Ring structure on the stable homotopy groups of spheres well-defined?

Published on 25 Mar 2026 - 12:38

score 125 · Answer 11 · 2026-04-14 09:00:33

125

Views

Understanding the explicit homotopy of Exercise 1.1.10

Published on 14 Apr 2026 - 9:00

score 60 · Answer 12 · 2023-02-05 17:05:37

60

Views

Let $F:B^2 \to B^2$ be a continuous map w/ $F(S^1)\subseteq S^1$, and let $f:S^1\to S^1$ be $f(z)=F(z)$. Prove $F$ is onto or $f$ is nullhomotopic.

Published on 05 Feb 2023 - 17:05

score 57 · Answer 13 · 2026-04-14 18:07:56

57

Views

Suppose $X$ is obtained from $A$ by attaching $(n+1)$-cells. Then $(X,A)$ is $n$-connected.

Published on 14 Apr 2026 - 18:07

score 429 · Answer 14 · 2026-04-14 13:13:32

429

Views

Non-contractible space, but all maps are homotopic

Published on 14 Apr 2026 - 13:13

score 76 · Answer 15 · 2026-04-11 14:56:43

76

Views

When is the induced map in a pullback diagram a fibration?

Published on 11 Apr 2026 - 14:56

List Question

Show that any continuous map $f: \mathbb{R}^n \rightarrow X$ is homotopic to the constant map

Connected one-dimensional CW complex and homotopy groups

Homology isomorphism between H-spaces

Split cofiber sequence

Let $X$ and $Y$ are copies of $S^2$ taking points $x_1,x_2 \in X$ and $y_1, y_2 \in Y$ then $\pi_1(X \bigsqcup Y/x_1\sim y_1,y_2\sim x_2 )?$

Homotopy fiber of a bundle

Killing Homology classes in 'controlled' way à la in Postnikov tower

Modification of a CW-Complex $X$ with control over Homology groups

Which homotopy colimits commute with finite homotopy limits?

Ring structure on the stable homotopy groups of spheres well-defined?

Understanding the explicit homotopy of Exercise 1.1.10

Let $F:B^2 \to B^2$ be a continuous map w/ $F(S^1)\subseteq S^1$, and let $f:S^1\to S^1$ be $f(z)=F(z)$. Prove $F$ is onto or $f$ is nullhomotopic.

Suppose $X$ is obtained from $A$ by attaching $(n+1)$-cells. Then $(X,A)$ is $n$-connected.

Non-contractible space, but all maps are homotopic

When is the induced map in a pullback diagram a fibration?

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