List questions from homotopy-theory

Published on 15 Apr 2026 - 5:32

219

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Example of cw complexes quasi isomorphic but not homotopic.

Published on 14 Apr 2026 - 8:48

114

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How to prove this ? I have tried to use $F$ but it doesn't fulfill the conditions. Thank you.

Published on 16 Apr 2026 - 3:18

37

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$S^k$ surrounding an $(n-k-1)$-plane in $\mathbb{R}^n$

Published on 16 Apr 2026 - 20:58

541

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Understanding Sheaves and Stacks

Published on 22 Apr 2026 - 0:57

519

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What is a pi mapping in topology?

Published on 10 Apr 2026 - 6:01

44

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1-cycles of $T^2$ distinguished by embedding

Published on 15 Apr 2026 - 5:00

94

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homotopic $C^{2}$ paths are $C^{2}$ homotopic?

Published on 14 Apr 2026 - 0:51

116

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Homotopy equivalence in relative Diffeomorphism group

Published on 25 Mar 2026 - 14:04

75

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Exercise 16.10. on pg.356 in "Modern Classical Homotopy Theory."

Published on 13 Apr 2026 - 17:13

114

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Show that $\pi_{i}(F) \cong \pi_{i +1}(X) $ where $F$ is the homotopy fiber of the inclusion $X \rightarrow X \times X.$

Published on 25 Mar 2026 - 12:29

182

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Monomorphisms and epimorphisms in a homotopy category

Published on 25 Apr 2026 - 12:22

79

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Determine with justification, whether $S^2 \times S^4$ is homeomorphic to $\mathbb{C}P^3$.

Published on 13 Apr 2026 - 2:55

330

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How to understand the definition of a final functor

Published on 25 Apr 2026 - 12:24

38

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On converting diagonal maps $X \rightarrow X \times ... \times X$ to fibrations.

Published on 16 Apr 2026 - 18:43

List Question

$CX\cup_{\overline f}CY$ is homeomorphis to reduced suspension $\Sigma X$

Example of cw complexes quasi isomorphic but not homotopic.

How to prove this ? I have tried to use $F$ but it doesn't fulfill the conditions. Thank you.

$S^k$ surrounding an $(n-k-1)$-plane in $\mathbb{R}^n$

Understanding Sheaves and Stacks

What is a pi mapping in topology?

1-cycles of $T^2$ distinguished by embedding

homotopic $C^{2}$ paths are $C^{2}$ homotopic?

Homotopy equivalence in relative Diffeomorphism group

Exercise 16.10. on pg.356 in "Modern Classical Homotopy Theory."

Show that $\pi_{i}(F) \cong \pi_{i +1}(X) $ where $F$ is the homotopy fiber of the inclusion $X \rightarrow X \times X.$

Monomorphisms and epimorphisms in a homotopy category

Determine with justification, whether $S^2 \times S^4$ is homeomorphic to $\mathbb{C}P^3$.

How to understand the definition of a final functor

On converting diagonal maps $X \rightarrow X \times ... \times X$ to fibrations.

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