List questions from homotopy-theory

Published on 11 May 2026 - 10:15

115

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If $G$ is a group of isometries of $X$ then prove that $X/G$ and $X/\bar{G}$ are homotopically equvalent

Published on 24 Apr 2026 - 5:08

984

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Reference request: homotopy groups of $\mathbb{C}P^n$ in terms of homotopy groups of spheres?

Published on 19 Oct 2015 - 20:22

581

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Formula relating Euler characteristics $\chi(A)$, $\chi(X)$, $\chi(Y)$, $\chi(Y \cup_f X)$ when $X$ and $Y$ are finite.

Published on 19 Oct 2015 - 20:28

206

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If $f(x) \neq g(x)$ for every $x ∈ S ^n$, then $g$ is homotopic to $a ◦ f$

Published on 20 Oct 2015 - 21:16

164

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Model category that doesn't admit functorial factorizations?

Published on 26 Apr 2026 - 9:55

57

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Given a map $h: S^n \to \mathbb{R}^{n+1}-{0}$ such that $x\cdot h(x)=0$ for all $x\in S^n$, $f:X\to S^n$ is homotopic to $-f$.

Published on 25 Oct 2015 - 23:13

712

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punctured real projective space

Published on 30 Mar 2026 - 21:04

1.3k

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For $X$ contractible, deformation retract of $CX$ onto $X$.

Published on 29 Oct 2015 - 1:42

599

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Homotopy classes of maps from projective plane to projective plane

Published on 29 Oct 2015 - 17:23

446

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Compression Criterion for $\pi_n(X,A,x_0)$. Why do we need homotopies $\text{rel} \ S^{n-1}$?

Published on 30 Oct 2015 - 10:50

1.6k

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Degree 1 maps from $\mathbb S^n$

Published on 30 Oct 2015 - 19:29

185

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Nice Categories of Based Topological Spaces Are Not Cartesian Closed

Published on 30 Oct 2015 - 19:29

103

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Random sphere-valued fields

Published on 02 Nov 2015 - 15:19

1.2k

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Degree of maps and coverings

Published on 03 Apr 2026 - 0:33

List Question

Is $Y \cup_f X$ a CW complex?

If $G$ is a group of isometries of $X$ then prove that $X/G$ and $X/\bar{G}$ are homotopically equvalent

Reference request: homotopy groups of $\mathbb{C}P^n$ in terms of homotopy groups of spheres?

Formula relating Euler characteristics $\chi(A)$, $\chi(X)$, $\chi(Y)$, $\chi(Y \cup_f X)$ when $X$ and $Y$ are finite.

If $f(x) \neq g(x)$ for every $x ∈ S ^n$, then $g$ is homotopic to $a ◦ f$

Model category that doesn't admit functorial factorizations?

Given a map $h: S^n \to \mathbb{R}^{n+1}-{0}$ such that $x\cdot h(x)=0$ for all $x\in S^n$, $f:X\to S^n$ is homotopic to $-f$.

punctured real projective space

For $X$ contractible, deformation retract of $CX$ onto $X$.

Homotopy classes of maps from projective plane to projective plane

Compression Criterion for $\pi_n(X,A,x_0)$. Why do we need homotopies $\text{rel} \ S^{n-1}$?

Degree 1 maps from $\mathbb S^n$

Nice Categories of Based Topological Spaces Are Not Cartesian Closed

Random sphere-valued fields

Degree of maps and coverings

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