List questions from homotopy-theory

Published on 09 Apr 2026 - 8:27

56

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Prove that a function defines homotopy equivalence

Published on 15 Apr 2026 - 5:24

270

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Collapsing an arc on a sphere (Reduced suspension and unreduced suspension are the same for spheres)

Published on 13 Apr 2026 - 12:00

112

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Transposing homeomorphism $S^1 \land S^1 \to S^1 \land S^1$ is a reflection of $S^2$

Published on 16 Apr 2026 - 6:12

290

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Show that for Abelian groups $G$ and $H, \bigl[K(G, n), K(H, n)\bigr] \cong \operatorname{Hom}(G, H).$

Published on 14 Apr 2026 - 0:56

129

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$\langle X,\Omega^2 K\rangle$ is abelian

Published on 25 Mar 2026 - 15:58

117

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I have a question about homotopy of the unit circumference with a point

Published on 13 Apr 2026 - 21:13

169

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paths are homologous , but are not freely homotopic

Published on 11 Apr 2026 - 10:01

101

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Is there a continuous odd function from $S^3$ to $S^1$?

Published on 12 Apr 2026 - 20:13

58

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Homotopy rel boundary of disks in knot complement $\times I$

Published on 26 Mar 2026 - 17:32

84

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Homology with local coefficients (question on Whitehead's proof)

Published on 13 Apr 2026 - 23:40

530

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When is the mapping telescope homotopy equivalent to the space?

Published on 11 Apr 2026 - 7:11

53

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Equivalent condition for deformation retraction

Published on 15 Apr 2026 - 12:53

179

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Finding the cofibration of the map $S^{1} \rightarrow *. $

Published on 09 Apr 2026 - 10:03

63

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Determining the homotopy colimit of the following diagram.

Published on 15 Apr 2026 - 3:33

List Question

Doubt in the proof of Lemma to prove No Retraction Theorem

Prove that a function defines homotopy equivalence

Collapsing an arc on a sphere (Reduced suspension and unreduced suspension are the same for spheres)

Transposing homeomorphism $S^1 \land S^1 \to S^1 \land S^1$ is a reflection of $S^2$

Show that for Abelian groups $G$ and $H, \bigl[K(G, n), K(H, n)\bigr] \cong \operatorname{Hom}(G, H).$

$\langle X,\Omega^2 K\rangle$ is abelian

I have a question about homotopy of the unit circumference with a point

paths are homologous , but are not freely homotopic

Is there a continuous odd function from $S^3$ to $S^1$?

Homotopy rel boundary of disks in knot complement $\times I$

Homology with local coefficients (question on Whitehead's proof)

When is the mapping telescope homotopy equivalent to the space?

Equivalent condition for deformation retraction

Finding the cofibration of the map $S^{1} \rightarrow *. $

Determining the homotopy colimit of the following diagram.

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