List questions from homotopy-theory

Published on 29 Apr 2026 - 12:51

73

Views

If a homotopy can be extended to a neighborhood of a closed subspace of a normal space $X$, then it can be extended to all of $X$.

Published on 29 Apr 2026 - 12:52

87

Views

If $\pi_0(X)=\pi_1(X)=0$ and $H_2(X)=0$ then is it true that $\pi_2(X)=0$?

Published on 15 Apr 2026 - 23:23

180

Views

Family of smooth Cumulative Distribution Functions on $\mathbb{R}^+$ with non-smooth limits

Published on 25 Mar 2026 - 16:03

23

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Null-homotopic function on a set

Published on 11 Apr 2026 - 11:29

34

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The quotient of $\pi_n(X,A,x_0)$ by the action of $\pi_1(X,A,x_0)$ is Abelian

Published on 14 Apr 2026 - 21:54

68

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Is there an isomorphism in long exact sequence of fibration, which arises from homotopy fiber construction?

Published on 25 Mar 2026 - 14:08

169

Views

Circle map homotopy

Published on 13 Apr 2026 - 4:21

79

Views

Showing $i_*:\pi_k(X^n, x_0) \to \pi_k(X, x_0)$ is injective for $k \le n-1$

Published on 16 Apr 2026 - 9:39

63

Views

Symmetric spectrum associated to a ring

Published on 25 Mar 2026 - 6:08

74

Views

Path in GL(V) induces a proper homotopy

Published on 10 Apr 2026 - 14:26

91

Views

What does it mean for this proposition to hold in $Top_*$?

Published on 25 Mar 2026 - 11:01

349

Views

Understanding suspension in the model category of chain complexes.

Published on 26 Apr 2026 - 11:08

322

Views

Homotopy of Jordan Curves?

Published on 11 Apr 2026 - 9:51

71

Views

Where is the loophole in this homotopy argument?

Published on 15 Apr 2026 - 3:51

List Question

any cofibration $i:A \to B$ is a homeomorphism onto its image (question regarding the inverse map)

If a homotopy can be extended to a neighborhood of a closed subspace of a normal space $X$, then it can be extended to all of $X$.

If $\pi_0(X)=\pi_1(X)=0$ and $H_2(X)=0$ then is it true that $\pi_2(X)=0$?

Family of smooth Cumulative Distribution Functions on $\mathbb{R}^+$ with non-smooth limits

Null-homotopic function on a set

The quotient of $\pi_n(X,A,x_0)$ by the action of $\pi_1(X,A,x_0)$ is Abelian

Is there an isomorphism in long exact sequence of fibration, which arises from homotopy fiber construction?

Circle map homotopy

Showing $i_*:\pi_k(X^n, x_0) \to \pi_k(X, x_0)$ is injective for $k \le n-1$

Symmetric spectrum associated to a ring

Path in GL(V) induces a proper homotopy

What does it mean for this proposition to hold in $Top_*$?

Understanding suspension in the model category of chain complexes.

Homotopy of Jordan Curves?

Where is the loophole in this homotopy argument?

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