Question

Space pairs $(D^n,S^{n-1})$ and $(\mathbb R^n,\mathbb R^n\backslash\{0\})$ are NOT homotopy equivalent

score 121 · Answer 1 · 2026-04-15 21:54:21

121

Views

Space pairs $(D^n,S^{n-1})$ and $(\mathbb R^n,\mathbb R^n\backslash\{0\})$ are NOT homotopy equivalent

Published on 15 Apr 2026 - 21:54

score 32 · Answer 2 · 2026-04-12 05:37:25

32

Views

Is there a notion of 'trapezoidal Cartesian product' suitable for homotopies?

Published on 12 Apr 2026 - 5:37

score 53 · Answer 3 · 2026-04-13 00:41:54

53

Views

Fundamental group of $n$-Manifold without one point

Published on 13 Apr 2026 - 0:41

score 54 · Answer 4 · 2026-04-12 14:10:33

54

Views

A simple connected domain -- proof without Van - Kampen's theorem?

Published on 12 Apr 2026 - 14:10

score 70 · Answer 5 · 2023-05-19 00:53:03

70

Views

Second homotopy group of a torus with a disc attached to it

Published on 19 May 2023 - 0:53

score 29 · Answer 6 · 2026-04-12 13:47:01

29

Views

Homotopy class for the summation of closed paths

Published on 12 Apr 2026 - 13:47

score 101 · Answer 7 · 2026-04-12 17:16:12

101

Views

Showing the Euler characteristic is homotopy invariant

Published on 12 Apr 2026 - 17:16

score 147 · Answer 8 · 2026-03-25 14:21:46

147

Views

Simple explicit example of higher Eilenberg-MacLane space

Published on 25 Mar 2026 - 14:21

score 49 · Answer 9 · 2026-04-16 05:45:24

49

Views

Closed curve not intersecting a disc means all points in the disk have the same winding number

Published on 16 Apr 2026 - 5:45

score 106 · Answer 10 · 2026-03-25 04:38:23

106

Views

Finite CW-complex with finite homotopy groups

Published on 25 Mar 2026 - 4:38

score 60 · Answer 11 · 2026-04-12 05:01:49

60

Views

Given a regular cover $Y\to X$ of sufficiently nice spaces, does the Deck transformation group act on $\pi_1(X)$?

Published on 12 Apr 2026 - 5:01

score 58 · Answer 12 · 2026-04-11 07:25:06

58

Views

Rolfsen exercise, torus knots

Published on 11 Apr 2026 - 7:25

score 95 · Answer 13 · 2026-04-10 05:58:36

95

Views

Do unit quaternions admit a continuous square root function?

Published on 10 Apr 2026 - 5:58

score 124 · Answer 14 · 2026-04-17 10:24:10

124

Views

Quillen pair with derived equivalence $\implies$ Quillen equivalence

Published on 17 Apr 2026 - 10:24

score 22 · Answer 15 · 2026-04-15 02:55:34

22

Views

Homotopy equivalence between product of circles and complements of kernels

Published on 15 Apr 2026 - 2:55

List Question

Space pairs $(D^n,S^{n-1})$ and $(\mathbb R^n,\mathbb R^n\backslash\{0\})$ are NOT homotopy equivalent

Is there a notion of 'trapezoidal Cartesian product' suitable for homotopies?

Fundamental group of $n$-Manifold without one point

A simple connected domain -- proof without Van - Kampen's theorem?

Second homotopy group of a torus with a disc attached to it

Homotopy class for the summation of closed paths

Showing the Euler characteristic is homotopy invariant

Simple explicit example of higher Eilenberg-MacLane space

Closed curve not intersecting a disc means all points in the disk have the same winding number

Finite CW-complex with finite homotopy groups

Given a regular cover $Y\to X$ of sufficiently nice spaces, does the Deck transformation group act on $\pi_1(X)$?

Rolfsen exercise, torus knots

Do unit quaternions admit a continuous square root function?

Quillen pair with derived equivalence $\implies$ Quillen equivalence

Homotopy equivalence between product of circles and complements of kernels

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