List questions from homotopy-theory

Published on 11 May 2026 - 7:46

173

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Calculating the homotopy groups of a complex

Published on 13 Apr 2026 - 1:14

784

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Who proved that existence of a retraction $r:X\times\mathbb{I}\rightarrow X\times\left\{ 0\right\} \cup A\times\mathbb{I}$ was sufficient for HEP?

Published on 16 Apr 2026 - 11:18

1.4k

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$A$ retract of $X$ and $X$ contractible implies $A$ contractible.

Published on 14 Apr 2026 - 1:11

752

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Are cofibrant/fibrant replacements homotopically unique?

Published on 17 Sep 2013 - 11:19

180

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$\pi_1(X)\cong \mathbb Z_{p^n}$

Published on 13 Apr 2026 - 8:57

88

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Let $\left(X,A\right)$ be a cofibered pair. Has pair $\left(X\times\left\{ t\right\} ,A\times\mathbb{I}\right)$ the gluing property?

Published on 16 Apr 2026 - 11:19

573

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Homotopy of a CW complex

Published on 15 May 2026 - 15:08

179

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Show that two different embeddings of the figure-eight in the torus are not homotopic

Published on 13 Apr 2026 - 22:03

1k

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Smooth torus eversion

Published on 15 Apr 2026 - 3:06

295

Views

Path homotopy in the plane

Published on 12 Apr 2026 - 22:11

409

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Can abstract nonsense be helpful here?

Published on 12 Apr 2026 - 8:53

193

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Should the first be the last by composition of paths?

Published on 11 May 2026 - 2:09

244

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Is the continuous map between CW-complexes a cofibration?

Published on 11 Apr 2026 - 5:23

1.6k

Views

Difference between free homotopy and isotopy. Numer of non-isotopic curves.

Published on 14 Apr 2026 - 15:57

List Question

Statement about Homotopy in Brown's "Topology & Groupoids"

Calculating the homotopy groups of a complex

Who proved that existence of a retraction $r:X\times\mathbb{I}\rightarrow X\times\left\{ 0\right\} \cup A\times\mathbb{I}$ was sufficient for HEP?

$A$ retract of $X$ and $X$ contractible implies $A$ contractible.

Are cofibrant/fibrant replacements homotopically unique?

$\pi_1(X)\cong \mathbb Z_{p^n}$

Let $\left(X,A\right)$ be a cofibered pair. Has pair $\left(X\times\left\{ t\right\} ,A\times\mathbb{I}\right)$ the gluing property?

Homotopy of a CW complex

Show that two different embeddings of the figure-eight in the torus are not homotopic

Smooth torus eversion

Path homotopy in the plane

Can abstract nonsense be helpful here?

Should the first be the last by composition of paths?

Is the continuous map between CW-complexes a cofibration?

Difference between free homotopy and isotopy. Numer of non-isotopic curves.

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