List questions from homotopy-theory

Published on 13 Apr 2026 - 19:37

355

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A question on the non trivial rank three bundle on $S^2$

Published on 16 Apr 2026 - 1:10

430

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Homotopy of closed curves is also a closed curve?

Published on 13 Apr 2026 - 10:57

228

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Second homotopy of $S^1\vee S^2 \vee T^2$

Published on 15 Apr 2026 - 14:35

340

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Let $G$ a simple connected topological group and $H$ a normal discrete subgroup, then $\pi_1(G/H,e) = H.$

Published on 12 Apr 2026 - 20:22

195

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Principal bundle as homotopy fiber universally self-trivializes

Published on 09 Apr 2026 - 23:27

43

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basepoint problem: Is there an action of $\pi_1(B)$ on $\pi_1(F)$ for $F$ path connected

Published on 10 Apr 2026 - 23:17

52

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Let $f:S^1 \to X$ a continuous function $X$ a topological space. Then $f$ is homotopic to a constant iff $f$ extends to $D$.

Published on 14 Apr 2026 - 16:32

305

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Why all differentials are $0$ for Serre Spectral Sequence of trivial fibration?

Published on 14 Apr 2026 - 18:40

147

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Counter-example for $\tilde{H} (X/A) \cong H (X, A)$?

Published on 09 Apr 2026 - 11:12

74

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Homotopy type of some lattices with top and bottom removed

Published on 15 Apr 2026 - 5:40

1.2k

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If two maps are homotopic, are the images homotopy equivalent?

Published on 16 Apr 2026 - 4:32

178

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$\pi_0(SO(N))$ and $\pi_0(O(N))$: Inconsistency between Bott periodicity and basic understanding of $\pi_0$

Published on 25 Mar 2026 - 11:04

78

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$f: S^n \to S^n$ is the restriction of a continuous mapping $F: \overline{B^n_1} \to S^n$ iff $deg(f) = 0$.

Published on 16 Apr 2026 - 16:20

233

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Homotopy: equivalence relation (continuity of homotopy in symmetry)

Published on 14 Apr 2026 - 0:52

List Question

Homotopy on a cylinder

A question on the non trivial rank three bundle on $S^2$

Homotopy of closed curves is also a closed curve?

Second homotopy of $S^1\vee S^2 \vee T^2$

Let $G$ a simple connected topological group and $H$ a normal discrete subgroup, then $\pi_1(G/H,e) = H.$

Principal bundle as homotopy fiber universally self-trivializes

basepoint problem: Is there an action of $\pi_1(B)$ on $\pi_1(F)$ for $F$ path connected

Let $f:S^1 \to X$ a continuous function $X$ a topological space. Then $f$ is homotopic to a constant iff $f$ extends to $D$.

Why all differentials are $0$ for Serre Spectral Sequence of trivial fibration?

Counter-example for $\tilde{H} (X/A) \cong H (X, A)$?

Homotopy type of some lattices with top and bottom removed

If two maps are homotopic, are the images homotopy equivalent?

$\pi_0(SO(N))$ and $\pi_0(O(N))$: Inconsistency between Bott periodicity and basic understanding of $\pi_0$

$f: S^n \to S^n$ is the restriction of a continuous mapping $F: \overline{B^n_1} \to S^n$ iff $deg(f) = 0$.

Homotopy: equivalence relation (continuity of homotopy in symmetry)

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