Question

an extension for one of two homotopic maps implies the existence of a homotopic extension for another map.

score 142 · Answer 1 · 2026-03-25 23:13:09

142

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an extension for one of two homotopic maps implies the existence of a homotopic extension for another map.

Published on 25 Mar 2026 - 23:13

score 61 · Answer 2 · 2026-03-25 23:10:02

61

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Let $C$ be a space such that $C=A \cup B$ and $A \cap B ↪ A$ is a cofibration. Show that $B ↪C$ is a cofibration.

Published on 25 Mar 2026 - 23:10

score 995 · Answer 3 · 2026-03-25 08:13:41

995

Views

Prove that $\pi_1(X\times Y, (x_0,y_0))$ is isomorphic to $\pi_1(X,x_0)\times \pi_1(Y,y_0)$.

Published on 25 Mar 2026 - 8:13

score 449 · Answer 4 · 2026-03-25 13:33:23

449

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Exercises 1.1.5 Algebraic Topology by Allen Hatcher

Published on 25 Mar 2026 - 13:33

score 112 · Answer 5 · 2026-04-01 08:36:58

112

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Homotopy equivalent prove

Published on 01 Apr 2026 - 8:36

score 137 · Answer 6 · 2026-03-26 02:48:59

137

Views

Let $\alpha:S^n\rightarrow S^n$ be the antipodal map. Why is $\alpha \not\simeq id$ if $n$ is even?

Published on 26 Mar 2026 - 2:48

score 269 · Answer 7 · 2026-04-09 00:31:32

269

Views

Necessary conditions for a Reedy fibrant diagram

Published on 09 Apr 2026 - 0:31

score 164 · Answer 8 · 2026-03-28 10:16:47

164

Views

Same homology and distinct homotopy on torus

Published on 28 Mar 2026 - 10:16

score 319 · Answer 9 · 2026-03-29 17:13:21

319

Views

Is the closed interval $[0,1]$ always needed to do homotopy?

Published on 29 Mar 2026 - 17:13

score 622 · Answer 10 · 2026-03-28 12:14:41

622

Views

A pushout of an acyclic cofibration is an acyclic cofibration

Published on 28 Mar 2026 - 12:14

score 201 · Answer 11 · 2026-04-09 02:00:43

201

Views

For simplicial abelian group quotient map to the quotient chain complex is homotopy equivalence.

Published on 09 Apr 2026 - 2:00

score 696 · Answer 12 · 2026-03-28 11:54:18

696

Views

A space $X$ is contractible if and only if it is homotopically equivalent to the space with one point.

Published on 28 Mar 2026 - 11:54

score 97 · Answer 13 · 2026-04-09 04:27:20

97

Views

Characterisation Fibration

Published on 09 Apr 2026 - 4:27

score 760 · Answer 14 · 2026-04-09 01:54:31

760

Views

Discrete simplicial set, definition

Published on 09 Apr 2026 - 1:54

score 37 · Answer 15 · 2026-04-01 12:37:47

37

Views

Homotopy Equivalences of Spaces?

Published on 01 Apr 2026 - 12:37

List Question

an extension for one of two homotopic maps implies the existence of a homotopic extension for another map.

Let $C$ be a space such that $C=A \cup B$ and $A \cap B ↪ A$ is a cofibration. Show that $B ↪C$ is a cofibration.

Prove that $\pi_1(X\times Y, (x_0,y_0))$ is isomorphic to $\pi_1(X,x_0)\times \pi_1(Y,y_0)$.

Exercises 1.1.5 Algebraic Topology by Allen Hatcher

Homotopy equivalent prove

Let $\alpha:S^n\rightarrow S^n$ be the antipodal map. Why is $\alpha \not\simeq id$ if $n$ is even?

Necessary conditions for a Reedy fibrant diagram

Same homology and distinct homotopy on torus

Is the closed interval $[0,1]$ always needed to do homotopy?

A pushout of an acyclic cofibration is an acyclic cofibration

For simplicial abelian group quotient map to the quotient chain complex is homotopy equivalence.

A space $X$ is contractible if and only if it is homotopically equivalent to the space with one point.

Characterisation Fibration

Discrete simplicial set, definition

Homotopy Equivalences of Spaces?

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