Question

The fundamental group of a half disk ( a neighborhood of a boundary point) can't be detected

score 43 · Answer 1 · 2018-10-10 16:46:03

43

Views

The fundamental group of a half disk ( a neighborhood of a boundary point) can't be detected

Published on 10 Oct 2018 - 16:46

score 718 · Answer 2 · 2026-03-22 12:48:21

718

Views

The fundamental group of Klein bottle/{3pt}

Published on 22 Mar 2026 - 12:48

score 30 · Answer 3 · 2018-10-17 12:22:14

30

Views

Fundamental group of a plane united with a circle in 3D space

Published on 17 Oct 2018 - 12:22

score 123 · Answer 4 · 2026-03-17 05:54:09

123

Views

Fundamental group of $K\# K/\{3\text{ points}\}$

Published on 17 Mar 2026 - 5:54

score 89 · Answer 5 · 2018-10-23 15:47:22

89

Views

Fundamental group of the union of a quadric and line

Published on 23 Oct 2018 - 15:47

score 596 · Answer 6 · 2026-03-25 03:02:58

596

Views

What are some other topological invariants apart from connectedness, compactness and fundamental groups?

Published on 25 Mar 2026 - 3:02

score 373 · Answer 7 · 2018-10-26 04:24:13

373

Views

Fundamental group of the union of subspaces

Published on 26 Oct 2018 - 4:24

score 99 · Answer 8 · 2018-11-04 13:22:18

99

Views

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

Published on 04 Nov 2018 - 13:22

score 86 · Answer 9 · 2018-11-05 04:34:34

86

Views

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

Published on 05 Nov 2018 - 4:34

score 959 · Answer 10 · 2018-11-07 10:15:34

959

Views

Let $\varphi: G \to G'$ be an injective homomorphism. If $G'$ is Abelian, then $G$ is Abelian? The context is fundamental groups.

Published on 07 Nov 2018 - 10:15

score 1.3k · Answer 11 · 2018-11-11 10:28:49

1.3k

Views

Prove "Contractible implies simply connected" using tools in Munkres Topology. Context is theta-space.

Published on 11 Nov 2018 - 10:28

score 579 · Answer 12 · 2026-03-25 12:50:12

579

Views

Fundamental group of theta-space and the doubly punctured theta space in Munkres Topology Example 70.1

Published on 25 Mar 2026 - 12:50

score 254 · Answer 13 · 2018-11-11 17:19:31

254

Views

Topological space with binary operation has abelian fundamental group

Published on 11 Nov 2018 - 17:19

score 83 · Answer 14 · 2026-02-23 02:59:27

83

Views

In theta space, is the lower arc and line segment a deformation retract of punctured theta?

Published on 23 Feb 2026 - 2:59

score 210 · Answer 15 · 2026-03-25 12:53:19

210

Views

Prove that doubly punctured theta space is contractible.

Published on 25 Mar 2026 - 12:53

List Question

The fundamental group of a half disk ( a neighborhood of a boundary point) can't be detected

The fundamental group of Klein bottle/{3pt}

Fundamental group of a plane united with a circle in 3D space

Fundamental group of $K\# K/\{3\text{ points}\}$

Fundamental group of the union of a quadric and line

What are some other topological invariants apart from connectedness, compactness and fundamental groups?

Fundamental group of the union of subspaces

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

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

Let $\varphi: G \to G'$ be an injective homomorphism. If $G'$ is Abelian, then $G$ is Abelian? The context is fundamental groups.

Prove "Contractible implies simply connected" using tools in Munkres Topology. Context is theta-space.

Fundamental group of theta-space and the doubly punctured theta space in Munkres Topology Example 70.1

Topological space with binary operation has abelian fundamental group

In theta space, is the lower arc and line segment a deformation retract of punctured theta?

Prove that doubly punctured theta space is contractible.

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