List questions from homotopy-theory

Published on 10 Apr 2026 - 23:33

327

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Is the $n^{\text{th}}$ homotopy group isomorphic to $[T^n, X]$

Published on 15 Apr 2026 - 4:39

104

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Intersection preserves homotopy equivalence

Published on 14 Apr 2026 - 6:33

38

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Lifting a homotopy class $S^k\to X$ into a simplicial set $X$ which is not fibrant but satisfies some weaker horn filling condition

Published on 13 Apr 2026 - 23:35

489

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inclusion of homotopy fiber and induced map on homology group

Published on 10 Apr 2026 - 11:23

3.2k

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Why is the unit circle, $\mathbf{S}^1$, a deformation retract of $\mathbf{R}^2$ minus any point?

Published on 16 Apr 2026 - 13:35

522

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Based space, commuting in diagram up to homotopy, dual Barratt-Puppe sequence.

Published on 17 Apr 2026 - 13:33

3.1k

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Algebraic Topology and Homotopy Theory prerequisites

Published on 13 Apr 2026 - 12:54

200

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Why $f$ and $g$ are still homotopic in $\mathbb R^2 - {\{O}\}$?

Published on 15 Apr 2026 - 18:23

188

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Let f and g be paths in R. Show that f is homotopic to g.

Published on 15 Apr 2026 - 13:57

207

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Prove that there is only one homotopy class of continuous functions from $X$ to $D$

Published on 15 Apr 2026 - 4:47

305

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Loop group of U(1)

Published on 09 Apr 2026 - 21:18

118

Views

Homotopy of maps to the product topology

Published on 14 Apr 2026 - 2:52

45

Views

What is the degree of $A(\theta)=\theta+\pi$?

Published on 09 Apr 2026 - 23:08

120

Views

Checking continuity for homotopy on glued space -- is it necessary?

Published on 12 Apr 2026 - 22:37

List Question

Homotopic family of curves

Is the $n^{\text{th}}$ homotopy group isomorphic to $[T^n, X]$

Intersection preserves homotopy equivalence

Lifting a homotopy class $S^k\to X$ into a simplicial set $X$ which is not fibrant but satisfies some weaker horn filling condition

inclusion of homotopy fiber and induced map on homology group

Why is the unit circle, $\mathbf{S}^1$, a deformation retract of $\mathbf{R}^2$ minus any point?

Based space, commuting in diagram up to homotopy, dual Barratt-Puppe sequence.

Algebraic Topology and Homotopy Theory prerequisites

Why $f$ and $g$ are still homotopic in $\mathbb R^2 - {\{O}\}$?

Let f and g be paths in R. Show that f is homotopic to g.

Prove that there is only one homotopy class of continuous functions from $X$ to $D$

Loop group of U(1)

Homotopy of maps to the product topology

What is the degree of $A(\theta)=\theta+\pi$?

Checking continuity for homotopy on glued space -- is it necessary?

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