List questions from homotopy-theory

Published on 25 Apr 2026 - 19:00

146

Views

Projective plane as a subcomplex of a 2-dimensional CW complex homotopy equivalent to $S^2$

Published on 12 Apr 2026 - 4:32

98

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Homotopy groups of real Grassmannians from their long exact sequence

Published on 13 Apr 2026 - 17:47

43

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Prove that if $f,g:S^1\to X$ are homotopic maps, then the spaces formed from $X$ by attaching a disc using $f$ and using $g$ are homotopy equivalent

Published on 15 Apr 2026 - 19:03

60

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Non-abelian cohomology

Published on 15 Apr 2026 - 7:04

93

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Can compact, non-hollow subsets of Euclidean space retract onto their topological boundary?

Published on 09 Apr 2026 - 13:55

44

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Intuition of Homotopy in Non-Euclidean Spaces

Published on 13 Apr 2026 - 21:29

40

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Example of a factorisation of functors $F = HK$ for which the Kan extension of $F$ along $K$ is not $H$.

Published on 26 Mar 2026 - 8:02

132

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Homotopy invariance of functors

Published on 11 Apr 2026 - 4:48

198

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Is there a manifold $M$ with nontrivial $\pi_2(M)$ but trivial $\pi_3(M)$?

Published on 14 Apr 2026 - 23:29

600

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For every sequence of homotopy groups is there a corresponding manifold?

Published on 14 Apr 2026 - 12:22

60

Views

Continuity of straight-line homotopy (for f,g: X to S where S is a convex set)

Published on 15 Apr 2026 - 2:41

58

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Category of Enriched $\mathcal{V}$-categories is a monoidal model category?

Published on 15 Apr 2026 - 20:02

137

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Homotopy fiber of the fold map

Published on 11 Apr 2026 - 0:44

78

Views

The fundamental group of the circle

Published on 12 Apr 2026 - 12:12

List Question

What is a 'cofiber sequence' in a triangulated category?

Projective plane as a subcomplex of a 2-dimensional CW complex homotopy equivalent to $S^2$

Homotopy groups of real Grassmannians from their long exact sequence

Prove that if $f,g:S^1\to X$ are homotopic maps, then the spaces formed from $X$ by attaching a disc using $f$ and using $g$ are homotopy equivalent

Non-abelian cohomology

Can compact, non-hollow subsets of Euclidean space retract onto their topological boundary?

Intuition of Homotopy in Non-Euclidean Spaces

Example of a factorisation of functors $F = HK$ for which the Kan extension of $F$ along $K$ is not $H$.

Homotopy invariance of functors

Is there a manifold $M$ with nontrivial $\pi_2(M)$ but trivial $\pi_3(M)$?

For every sequence of homotopy groups is there a corresponding manifold?

Continuity of straight-line homotopy (for f,g: X to S where S is a convex set)

Category of Enriched $\mathcal{V}$-categories is a monoidal model category?

Homotopy fiber of the fold map

The fundamental group of the circle

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