List questions from homotopy-theory

Published on 10 Apr 2026 - 20:44

65

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Show that if $\{y_0\} \to Y$ is a cofibration, then $f$ has a homotopy inverse $g$ for which $g(y_0)=x_0$.

Published on 15 Apr 2026 - 3:56

54

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$\eta$-completed and $\eta$-inverted $KGL$

Published on 17 Apr 2026 - 6:18

90

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Does homotopy type of a map $S^1 \to RP^1$ defines a homotopy type of $(D^2, S^1)\to (RP^2, RP^1)$?

Published on 16 Apr 2026 - 2:10

101

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Composition of cofibrations is a cofibration

Published on 08 Apr 2026 - 16:11

119

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Mod p homology of extended powers

Published on 13 Apr 2026 - 17:51

106

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Long exact sequence of a Serre fibration

Published on 15 Apr 2026 - 19:23

70

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B of a pseudo-group

Published on 30 Apr 2026 - 9:28

46

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What is $\pi_3(SU(4)/SU(2))$?

Published on 18 Apr 2026 - 2:46

56

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Suppose $i: A ֒\to X$ is a cofibration and $Y$ is contractible. Prove that every map $f:A \to Y$ has an extension $g:X \to Y$.

Published on 15 Apr 2026 - 9:28

108

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Ranking topological invariants by "strength?"

Published on 25 Mar 2026 - 9:24

34

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Higher connectedness of product of CW complex

Published on 08 Apr 2026 - 16:40

77

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On suspension of real projective spaces

Published on 15 Apr 2026 - 1:14

107

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Suppose that $p :X \to B$ is a fibration and $Y$ is a contractible space. Show that every map $f:Y \to B$ has a lift $g:Y \to X$.

Published on 16 Apr 2026 - 1:12

163

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Can one find commuting homotopies of maps?

Published on 11 Apr 2026 - 11:01

List Question

Homotopy equivalent Kan complexes have homotopy equivalent "path spaces"

Show that if $\{y_0\} \to Y$ is a cofibration, then $f$ has a homotopy inverse $g$ for which $g(y_0)=x_0$.

$\eta$-completed and $\eta$-inverted $KGL$

Does homotopy type of a map $S^1 \to RP^1$ defines a homotopy type of $(D^2, S^1)\to (RP^2, RP^1)$?

Composition of cofibrations is a cofibration

Mod p homology of extended powers

Long exact sequence of a Serre fibration

B of a pseudo-group

What is $\pi_3(SU(4)/SU(2))$?

Suppose $i: A ֒\to X$ is a cofibration and $Y$ is contractible. Prove that every map $f:A \to Y$ has an extension $g:X \to Y$.

Ranking topological invariants by "strength?"

Higher connectedness of product of CW complex

On suspension of real projective spaces

Suppose that $p :X \to B$ is a fibration and $Y$ is a contractible space. Show that every map $f:Y \to B$ has a lift $g:Y \to X$.

Can one find commuting homotopies of maps?

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