List questions from retraction

Published on 15 Feb 2021 - 19:55

272

Views

The fundamental group of $S^3 \setminus (\text{Hopf link})$ is $\mathbb{Z}^2$.

Published on 09 Apr 2021 - 19:27

79

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How to show that $X - \{0\}$ deformation retracts to $Y\ $?

Published on 27 Apr 2021 - 19:42

166

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Finding an explicit deformation from the mapping cylinder onto $Y.$

Published on 28 Apr 2021 - 17:29

83

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How to show that $\mathbb{R}^3$ with two disjoint parallel lines removed has the same homotopy type as $N$.

Published on 28 Apr 2021 - 19:10

163

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Retraction between wedge sum and product of spaces

Published on 04 May 2021 - 21:11

129

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${\pi_1(\mathbb{R}^3 \setminus A)}$ where $A$ is a circle in ${\mathbb{R}^3}$

Published on 11 May 2021 - 20:12

226

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Homotopic attaching maps induce spaces of same homotopy type.

Published on 18 May 2021 - 15:57

171

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A question about retraction of the torus onto the cylinder.

Published on 12 Jun 2021 - 5:58

140

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Why can't there be a retraction $r:D\to S^1$ from a disk to its boundary?

Published on 23 Jun 2021 - 10:37

54

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$\mathbb C P^n - p \simeq \mathbb C P^{n-1}$ if $p \in \text {int} (D^{2n}).$

Published on 30 Jun 2021 - 6:17

433

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Suspension homomorphism

Published on 14 Jul 2021 - 7:36

455

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Reduced and unreduced suspension are homotopically equivalent

Published on 23 Feb 2026 - 8:39

167

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Infinite concatenation of homotopy

Published on 09 Aug 2021 - 16:53

186

Views

When does a contractible simple loop have a contraction where every intervening loop is simple?

Published on 21 Sep 2021 - 19:51

List Question

Find strong deformation retract to corona/crown

The fundamental group of $S^3 \setminus (\text{Hopf link})$ is $\mathbb{Z}^2$.

How to show that $X - \{0\}$ deformation retracts to $Y\ $?

Finding an explicit deformation from the mapping cylinder onto $Y.$

How to show that $\mathbb{R}^3$ with two disjoint parallel lines removed has the same homotopy type as $N$.

Retraction between wedge sum and product of spaces

${\pi_1(\mathbb{R}^3 \setminus A)}$ where $A$ is a circle in ${\mathbb{R}^3}$

Homotopic attaching maps induce spaces of same homotopy type.

A question about retraction of the torus onto the cylinder.

Why can't there be a retraction $r:D\to S^1$ from a disk to its boundary?

$\mathbb C P^n - p \simeq \mathbb C P^{n-1}$ if $p \in \text {int} (D^{2n}).$

Suspension homomorphism

Reduced and unreduced suspension are homotopically equivalent

Infinite concatenation of homotopy

When does a contractible simple loop have a contraction where every intervening loop is simple?

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