Question

Prove that $S^n /\{p,q\}$ is homotopy equivalent to $S^n \vee S^1$.

score 212 · Answer 1 · 2018-11-03 15:01:12

212

Views

Prove that $S^n /\{p,q\}$ is homotopy equivalent to $S^n \vee S^1$.

Published on 03 Nov 2018 - 15:01

score 90 · Answer 2 · 2018-11-03 16:36:56

90

Views

The boundary of a tetrahedron minus one facet is homeomorphic to a triangle

Published on 03 Nov 2018 - 16:36

score 134 · Answer 3 · 2018-11-03 16:47:06

134

Views

Prove that $λ(A)^+ : S^n → S^n$ (the map induced on one-point compactifications) is homotopic to identity if $\det(A) > 0$

Published on 03 Nov 2018 - 16:47

score 347 · Answer 4 · 2026-03-25 05:00:08

347

Views

Klein bottle is homeomorphic to unit square quotient

Published on 25 Mar 2026 - 5:00

score 939 · Answer 5 · 2018-11-04 02:58:36

939

Views

How to prove (rigorously) that these spaces are homotopy equivalent?

Published on 04 Nov 2018 - 2:58

score 75 · Answer 6 · 2026-04-04 01:29:42

75

Views

Lifting problem of a map $g:M\to B^2\mathbb{Z}_n$ to $f:M\to BPSU(n)$

Published on 04 Apr 2026 - 1:29

score 71 · Answer 7 · 2026-03-25 01:37:45

71

Views

Extend the fiber of a principal $PSU(n)$-bundle

Published on 25 Mar 2026 - 1:37

score 248 · Answer 8 · 2018-11-04 08:15:51

248

Views

Is the restriction of a map representing a cohomology class on its Poincare dual null-homotopic?

Published on 04 Nov 2018 - 8:15

score 100 · Answer 9 · 2026-03-25 20:41:43

100

Views

Example for a covering map with not equal groups from different base points

Published on 25 Mar 2026 - 20:41

score 264 · Answer 10 · 2018-11-04 14:07:46

264

Views

Example of a fibration that is not a fibre bundle

Published on 04 Nov 2018 - 14:07

score 449 · Answer 11 · 2018-11-04 15:38:05

449

Views

Does semi-locally simply connected imply locally path connected?

Published on 04 Nov 2018 - 15:38

score 98 · Answer 12 · 2018-11-04 16:50:07

98

Views

What would be the water-line of a Klein bottle afloat in the sea?

Published on 04 Nov 2018 - 16:50

score 39 · Answer 13 · 2026-03-31 13:16:05

39

Views

Showing that interior of a cover of a topological space being a cover is essential to guarantee an isomorphism between homology groups

Published on 31 Mar 2026 - 13:16

score 79 · Answer 14 · 2026-03-27 02:32:22

79

Views

Retract of Compact $2$-manifold

Published on 27 Mar 2026 - 2:32

score 87 · Answer 15 · 2026-03-25 22:06:02

87

Views

Prove that there is a bijective correspondence between $π_1(X,x_0)$ and $π_1(X;x_0 → x_1 )$

Published on 25 Mar 2026 - 22:06

List Question

Prove that $S^n /\{p,q\}$ is homotopy equivalent to $S^n \vee S^1$.

The boundary of a tetrahedron minus one facet is homeomorphic to a triangle

Prove that $λ(A)^+ : S^n → S^n$ (the map induced on one-point compactifications) is homotopic to identity if $\det(A) > 0$

Klein bottle is homeomorphic to unit square quotient

How to prove (rigorously) that these spaces are homotopy equivalent?

Lifting problem of a map $g:M\to B^2\mathbb{Z}_n$ to $f:M\to BPSU(n)$

Extend the fiber of a principal $PSU(n)$-bundle

Is the restriction of a map representing a cohomology class on its Poincare dual null-homotopic?

Example for a covering map with not equal groups from different base points

Example of a fibration that is not a fibre bundle

Does semi-locally simply connected imply locally path connected?

What would be the water-line of a Klein bottle afloat in the sea?

Showing that interior of a cover of a topological space being a cover is essential to guarantee an isomorphism between homology groups

Retract of Compact $2$-manifold

Prove that there is a bijective correspondence between $π_1(X,x_0)$ and $π_1(X;x_0 → x_1 )$

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