Question

Torus with one disk attached inside

score 69 · Answer 1 · 2023-07-24 17:54:46

69

Views

Torus with one disk attached inside

Published on 24 Jul 2023 - 17:54

score 60 · Answer 2 · 2023-07-25 01:55:11

60

Views

Seifert–Van Kampen theorem on gluing two solid torus

Published on 25 Jul 2023 - 1:55

score 77 · Answer 3 · 2023-07-25 03:38:27

77

Views

Difficulty understanding how to deform these oriented circles continuously and make the following links (would like a drawing):

Published on 25 Jul 2023 - 3:38

score 101 · Answer 4 · 2026-03-28 22:55:07

101

Views

If $X$ has $S^{2n}$ as universal covering space then $\pi_1(X)$ is trivial or $\mathbb{Z}/2\mathbb{Z}$.

Published on 28 Mar 2026 - 22:55

score 76 · Answer 5 · 2023-07-29 09:38:57

76

Views

If every map $I\to S^1$ is nullhomotopic, then $\pi_1(S^1)$ is trivial?

Published on 29 Jul 2023 - 9:38

score 124 · Answer 6 · 2023-07-31 20:12:51

124

Views

Two surfaces with same homology groups but different fundamental group

Published on 31 Jul 2023 - 20:12

score 44 · Answer 7 · 2023-08-01 10:16:05

44

Views

Non-abelian subgroup of PSL(2,C) is discrete?

Published on 01 Aug 2023 - 10:16

score 121 · Answer 8 · 2026-03-27 18:28:00

121

Views

If a closed subset $C \subseteq \mathbb R^2$ is "fragilely"/“minimally” simple connected, must it be all of $\mathbb R^2$?

Published on 27 Mar 2026 - 18:28

score 223 · Answer 9 · 2023-08-07 02:19:37

223

Views

Is simple connectedness of subsets of $\mathbb{R}^2$ detected by winding numbers?

Published on 07 Aug 2023 - 2:19

score 107 · Answer 10 · 2023-08-15 11:05:38

107

Views

The fundamental group of the $n$-th symmetric product of $\mathbb{R}$: $\mathbb{R}^n/S_n$

Published on 15 Aug 2023 - 11:05

score 34 · Answer 11 · 2023-08-21 20:27:46

34

Views

Generator of fundamental group of the circle :

Published on 21 Aug 2023 - 20:27

score 70 · Answer 12 · 2023-08-22 18:48:25

70

Views

Find a space with same homology and fundamental group as a torus

Published on 22 Aug 2023 - 18:48

score 70 · Answer 13 · 2026-03-27 05:39:09

70

Views

Three questions about Wikipedia's definition of Van Kampen's theorem for fundamental groups

Published on 27 Mar 2026 - 5:39

score 68 · Answer 14 · 2023-08-28 20:49:44

68

Views

Proving that an isotopy of $\mathbb{R}^{2}$ must preserve orientation of an embedded circle.

Published on 28 Aug 2023 - 20:49

score 60 · Answer 15 · 2023-08-29 11:06:33

60

Views

Fiber functors and lifting property of coverings

Published on 29 Aug 2023 - 11:06

List Question

Torus with one disk attached inside

Seifert–Van Kampen theorem on gluing two solid torus

Difficulty understanding how to deform these oriented circles continuously and make the following links (would like a drawing):

If $X$ has $S^{2n}$ as universal covering space then $\pi_1(X)$ is trivial or $\mathbb{Z}/2\mathbb{Z}$.

If every map $I\to S^1$ is nullhomotopic, then $\pi_1(S^1)$ is trivial?

Two surfaces with same homology groups but different fundamental group

Non-abelian subgroup of PSL(2,C) is discrete?

If a closed subset $C \subseteq \mathbb R^2$ is "fragilely"/“minimally” simple connected, must it be all of $\mathbb R^2$?

Is simple connectedness of subsets of $\mathbb{R}^2$ detected by winding numbers?

The fundamental group of the $n$-th symmetric product of $\mathbb{R}$: $\mathbb{R}^n/S_n$

Generator of fundamental group of the circle :

Find a space with same homology and fundamental group as a torus

Three questions about Wikipedia's definition of Van Kampen's theorem for fundamental groups

Proving that an isotopy of $\mathbb{R}^{2}$ must preserve orientation of an embedded circle.

Fiber functors and lifting property of coverings

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