List questions from homotopy-theory

Published on 12 Apr 2026 - 11:19

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Hatcher, p.35, $\mathbb{R^{n}} - \{x\}$ is homeomorphic to $S^{n-1} \times \mathbb{R}$

Published on 14 Apr 2026 - 5:01

151

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Are there any stable $(\infty,1)$-topoi?

Published on 11 Apr 2026 - 7:30

82

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Homotopy product

Published on 12 Apr 2026 - 14:46

2.6k

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$X$ is contractible and $Y$ is path connected then $[X,Y]$ has a single point

Published on 13 Apr 2026 - 16:28

8.9k

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Homotopy groups of a wedge sum

Published on 10 Apr 2026 - 20:44

352

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Is the homology theory given by Eilenberg Maclane spectrum equal to ordinary homology?

Published on 25 Mar 2026 - 23:43

366

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smash product of Eilenberg-Maclane spaces

Published on 14 Apr 2026 - 19:24

915

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cells of quotient CW complex

Published on 14 Apr 2026 - 0:36

253

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Can one prove that $\Bbb{CP}^\infty$ is a $K(\Bbb Z, 2)$ without invoking the long exact sequence of a fibration?

Published on 13 Apr 2026 - 17:26

427

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Homotopical classes of mappings $\mathbb{CP}^n \to \mathbb{CP}^m$

Published on 15 Apr 2026 - 3:35

2.3k

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Are there nontrivial continuous maps between complex projective spaces?

Published on 10 Apr 2026 - 8:47

422

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Is an configuration space contractible?

Published on 10 Apr 2026 - 3:07

304

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Lifting cohomology-killing maps through the 3-sphere

Published on 14 Apr 2026 - 17:42

276

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A question on finite non-contractible CW complexes

Published on 15 Apr 2026 - 12:54

List Question

Motivation for the proof of the associativity of multiplication of equivalence classes of paths

Hatcher, p.35, $\mathbb{R^{n}} - \{x\}$ is homeomorphic to $S^{n-1} \times \mathbb{R}$

Are there any stable $(\infty,1)$-topoi?

Homotopy product

$X$ is contractible and $Y$ is path connected then $[X,Y]$ has a single point

Homotopy groups of a wedge sum

Is the homology theory given by Eilenberg Maclane spectrum equal to ordinary homology?

smash product of Eilenberg-Maclane spaces

cells of quotient CW complex

Can one prove that $\Bbb{CP}^\infty$ is a $K(\Bbb Z, 2)$ without invoking the long exact sequence of a fibration?

Homotopical classes of mappings $\mathbb{CP}^n \to \mathbb{CP}^m$

Are there nontrivial continuous maps between complex projective spaces?

Is an configuration space contractible?

Lifting cohomology-killing maps through the 3-sphere

A question on finite non-contractible CW complexes

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