List questions from homotopy-theory

Published on 12 Apr 2026 - 8:33

2.1k

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A question concerning fundamental groups and whether a map is null-homotopic.

Published on 14 Apr 2026 - 1:10

331

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Homotopy equivalence of torus and $\mathbb{C^2}$ without coordinate cross.

Published on 14 Apr 2026 - 19:51

625

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Is it true that any two tame knots are homotopic?

Published on 12 Apr 2026 - 6:59

314

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Question regarding the reduced suspension functor

Published on 11 May 2026 - 9:43

654

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Computation of the hom-set of a comodule over a coalgebra: $Ext_{E(x)}(k, E(x)) = P(y)$.

Published on 26 Mar 2026 - 4:53

118

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Are these 2 paths homotopic?

Published on 11 Apr 2026 - 6:32

57

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How to show $\mathbb{S}^{2n-1}$ is a $\mathbb{S}^{n-1}$ bundle over $\mathbb{S}^{n}$ then $n=1,2$ or divisible by $4$?

Published on 15 Apr 2026 - 3:50

1.9k

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Every principal $G$-bundle over a surface is trivial if $G$ is compact and simply connected: reference?

Published on 25 Mar 2026 - 22:03

622

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introductory reference for Hopf Fibrations

Published on 14 Apr 2026 - 10:51

4.2k

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$SU(n)$ is simply connected (proof without fibrations, $n>2$)

Published on 11 Apr 2026 - 7:41

1.1k

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What is the homotopy colimit of the Cech nerve as a bi-simplical set?

Published on 12 Apr 2026 - 16:05

120

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Naive question: Why $B:Mon\rightarrow Top^{}, \Omega: Top^{}\rightarrow Mon$ is an adjoint functor?

Published on 14 Apr 2026 - 23:58

3.1k

Views

What's the point of spectra?

Published on 25 Mar 2026 - 22:04

903

Views

Visualize Fourth Homotopy Group of $S^2$

Published on 16 Apr 2026 - 9:12

List Question

Proof for nonhomotopy

A question concerning fundamental groups and whether a map is null-homotopic.

Homotopy equivalence of torus and $\mathbb{C^2}$ without coordinate cross.

Is it true that any two tame knots are homotopic?

Question regarding the reduced suspension functor

Computation of the hom-set of a comodule over a coalgebra: $Ext_{E(x)}(k, E(x)) = P(y)$.

Are these 2 paths homotopic?

How to show $\mathbb{S}^{2n-1}$ is a $\mathbb{S}^{n-1}$ bundle over $\mathbb{S}^{n}$ then $n=1,2$ or divisible by $4$?

Every principal $G$-bundle over a surface is trivial if $G$ is compact and simply connected: reference?

introductory reference for Hopf Fibrations

$SU(n)$ is simply connected (proof without fibrations, $n>2$)

What is the homotopy colimit of the Cech nerve as a bi-simplical set?

Naive question: Why $B:Mon\rightarrow Top^{}, \Omega: Top^{}\rightarrow Mon$ is an adjoint functor?

What's the point of spectra?

Visualize Fourth Homotopy Group of $S^2$

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