List questions from homotopy-theory

Published on 13 Apr 2026 - 19:59

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Homotopy extension property and contractibility

Published on 12 Apr 2026 - 14:46

592

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The two-sided simplicial bar construction is Reedy-cofibrant

Published on 28 Mar 2026 - 21:27

804

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Free crossed modules

Published on 14 Apr 2026 - 23:31

211

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2-connected map between a connected sum and a gluing along one point.

Published on 13 Apr 2026 - 12:43

815

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Loop spaces and filtered colimits

Published on 11 May 2026 - 8:43

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Prove that any two maps $f, g:X \to Y$ are homotopic

Published on 15 Apr 2026 - 5:25

86

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Which is the functor of this limit?

Published on 16 Apr 2026 - 4:57

356

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On the commutativity of the relative homotopy groups

Published on 16 Apr 2026 - 13:53

161

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simple proposition about homotopy group

Published on 12 Apr 2026 - 2:11

320

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How are sets "trees with no symmetries"

Published on 11 Apr 2026 - 7:47

472

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Inclusion $O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C}) $

Published on 14 Apr 2026 - 3:46

2.8k

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Continuous maps from $S^1 \to X$ equivalent conditions

Published on 12 Apr 2026 - 18:14

336

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Computing $\pi_3(\mathrm{Gr}_2(\mathbb{R}^4))$

Published on 13 Apr 2026 - 12:04

908

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Examples of failure of excision for homotopy groups ($\pi_k(X, A)$ is not $\pi_k(X/A, *)$)

Published on 10 Apr 2026 - 8:21

List Question

Acyclic Hurewicz fibrations

Homotopy extension property and contractibility

The two-sided simplicial bar construction is Reedy-cofibrant

Free crossed modules

2-connected map between a connected sum and a gluing along one point.

Loop spaces and filtered colimits

Prove that any two maps $f, g:X \to Y$ are homotopic

Which is the functor of this limit?

On the commutativity of the relative homotopy groups

simple proposition about homotopy group

How are sets "trees with no symmetries"

Inclusion $O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C}) $

Continuous maps from $S^1 \to X$ equivalent conditions

Computing $\pi_3(\mathrm{Gr}_2(\mathbb{R}^4))$

Examples of failure of excision for homotopy groups ($\pi_k(X, A)$ is not $\pi_k(X/A, *)$)

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