List questions from homotopy-theory

Published on 11 Apr 2026 - 4:12

59

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Statement from Proposition 0.18 of Hatcher

Published on 09 Apr 2026 - 16:16

47

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A spectrum $X$ whose cohomology is $H^*(X; \mathbb{F}_2) = A//A(n)$

Published on 15 Apr 2026 - 15:31

61

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Elements of $\infty$-cats Corollary 4.1.3

Published on 11 Apr 2026 - 20:18

30

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differential graded nerve of a category whose mapping complexes are non-positive

Published on 16 Apr 2026 - 2:06

44

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Question About Independence Of Complex Contour Integral Over Homotopic Path.

Published on 10 Apr 2026 - 14:40

82

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Equivalence between the category $\text{Ho}(\mathcal{M})$ and $\text{Ho}(\mathcal{M}_{\mathcal{F}})$

Published on 25 Apr 2026 - 22:24

125

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Space homotopy equivalent to its own suspension is contractible

Published on 13 Apr 2026 - 4:48

53

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Is there a modern explanation of how Whitehead calculated $\pi_2^s$?

Published on 11 Apr 2026 - 22:37

49

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Uniqueness in Seifert-van Kampen theorem in Munkres' Topology

Published on 14 Apr 2026 - 0:33

45

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Seifert-van Kampen theorem, classical version

Published on 14 Apr 2026 - 19:05

57

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Connection between homology and homotopy invariants?

Published on 12 Apr 2026 - 4:08

98

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Prove that if a smooth manifold $M$ is contractible then every vector bundle over $M$ is trivial

Published on 16 Apr 2026 - 18:51

71

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Point-set level object/category

Published on 17 Apr 2026 - 3:38

66

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The fundamental group of $\Pi_{n=1}^\infty S^1$ with the $\operatorname{sup}$-metric

Published on 14 Apr 2026 - 5:14

List Question

Does being homotopic to $0$ imply being homologous to $0$ or viceversa?

Statement from Proposition 0.18 of Hatcher

A spectrum $X$ whose cohomology is $H^*(X; \mathbb{F}_2) = A//A(n)$

Elements of $\infty$-cats Corollary 4.1.3

differential graded nerve of a category whose mapping complexes are non-positive

Question About Independence Of Complex Contour Integral Over Homotopic Path.

Equivalence between the category $\text{Ho}(\mathcal{M})$ and $\text{Ho}(\mathcal{M}_{\mathcal{F}})$

Space homotopy equivalent to its own suspension is contractible

Is there a modern explanation of how Whitehead calculated $\pi_2^s$?

Uniqueness in Seifert-van Kampen theorem in Munkres' Topology

Seifert-van Kampen theorem, classical version

Connection between homology and homotopy invariants?

Prove that if a smooth manifold $M$ is contractible then every vector bundle over $M$ is trivial

Point-set level object/category

The fundamental group of $\Pi_{n=1}^\infty S^1$ with the $\operatorname{sup}$-metric

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