List questions from fundamental-groups

Published on 23 Feb 2026 - 20:40

358

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Fundamental Group of a Space obtained by attaching Two Cylinders

Published on 23 Oct 2022 - 9:49

82

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Show that the index is 2 if and only if $\tilde{X}$ is path-connected. Show that the index is 1 if and only if $\tilde{X} \cong X\sqcup X$

Published on 24 Oct 2022 - 17:31

93

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The complement of an algebraic curve is path-connected

Published on 26 Oct 2022 - 7:07

44

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A question related to a union of topological spaces

Published on 29 Oct 2022 - 13:38

66

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A surface formed by the union of two surfaces

Published on 29 Oct 2022 - 22:29

67

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How to prove orbifold fundamental group of a "basic orbifold" is a group

Published on 23 Feb 2026 - 10:03

75

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$S^2 \times S^2 \to S^2 \vee S^2 \vee S^4$

Published on 02 Nov 2022 - 9:54

67

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Is the complementary of the circunference simply connected

Published on 02 Nov 2022 - 19:14

178

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Is $G*G \cong G$ where $G$ is the fundamental group of the Hawaiian earring?

Published on 26 Mar 2026 - 6:15

59

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Fundamental Group of Vertices of a polygon identified to a point

Published on 18 Nov 2022 - 20:46

64

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Calculating Fundamental Group, using Van Kampen

Published on 19 Nov 2022 - 15:58

124

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When can a class in the fundamental group of a manifold be represented by an embedded loop?

Published on 28 Mar 2026 - 14:44

50

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Show that $\pi_1$ of this cover is a normal subgroup with index $\mathbb{Z}$

Published on 22 Nov 2022 - 17:04

156

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Why is $\pi_1 (S^n) = 0$ for $n \ge 2$?

Published on 30 Mar 2026 - 23:11

List Question

A question related to an induced homomorphism between two groups

Fundamental Group of a Space obtained by attaching Two Cylinders

Show that the index is 2 if and only if $\tilde{X}$ is path-connected. Show that the index is 1 if and only if $\tilde{X} \cong X\sqcup X$

The complement of an algebraic curve is path-connected

A question related to a union of topological spaces

A surface formed by the union of two surfaces

How to prove orbifold fundamental group of a "basic orbifold" is a group

$S^2 \times S^2 \to S^2 \vee S^2 \vee S^4$

Is the complementary of the circunference simply connected

Is $G*G \cong G$ where $G$ is the fundamental group of the Hawaiian earring?

Fundamental Group of Vertices of a polygon identified to a point

Calculating Fundamental Group, using Van Kampen

When can a class in the fundamental group of a manifold be represented by an embedded loop?

Show that $\pi_1$ of this cover is a normal subgroup with index $\mathbb{Z}$

Why is $\pi_1 (S^n) = 0$ for $n \ge 2$?

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