Question

Proof that the edge group $E(K,v)$ of a simplicial complex is isomorphic to the fundamental group $\pi_1 (|K|,v)$ of its polyhedron.

score 203 · Answer 1 · 2026-03-26 06:01:39

203

Views

Proof that the edge group $E(K,v)$ of a simplicial complex is isomorphic to the fundamental group $\pi_1 (|K|,v)$ of its polyhedron.

Published on 26 Mar 2026 - 6:01

score 260 · Answer 2 · 2020-01-26 11:44:51

260

Views

Van Kampen Theorem proof in Hatcher's book

Published on 26 Jan 2020 - 11:44

score 93 · Answer 3 · 2020-01-28 18:38:48

93

Views

Manifold with infinitely many based loops but only two unbased loops (up to homotopy).

Published on 28 Jan 2020 - 18:38

score 627 · Answer 4 · 2020-01-29 22:08:52

627

Views

Generator of a fundamental group Algebraic Topology

Published on 29 Jan 2020 - 22:08

score 1.7k · Answer 5 · 2020-01-30 02:58:01

1.7k

Views

Example of finite fundamental group

Published on 30 Jan 2020 - 2:58

score 98 · Answer 6 · 2020-01-30 16:44:31

98

Views

Isomorphism between fundamental group with end points of path as base points

Published on 30 Jan 2020 - 16:44

score 243 · Answer 7 · 2020-02-06 09:52:43

243

Views

Fundamental group of a space minus a point

Published on 06 Feb 2020 - 9:52

score 208 · Answer 8 · 2020-02-06 11:07:03

208

Views

Fundamental group of covering space given fundamental group of base

Published on 06 Feb 2020 - 11:07

score 76 · Answer 9 · 2020-02-06 15:23:22

76

Views

Fundamental group of a planar set: torsion free and no $\mathbb Z^2$ subgroup?

Published on 06 Feb 2020 - 15:23

score 91 · Answer 10 · 2020-02-21 03:38:36

91

Views

What does the notation $\pi_n(X) = 0$ and $\pi_n(X) = 1$ mean for a homotopy group?

Published on 21 Feb 2020 - 3:38

score 329 · Answer 11 · 2020-02-28 05:45:05

329

Views

Tammo tom Dieck's Algebraic Topology - van Kampen theorem for groupoids

Published on 28 Feb 2020 - 5:45

score 61 · Answer 12 · 2020-03-02 20:45:04

61

Views

Fundamental group of $(A \sqcup B)/\{A \ni (z,0) \sim (z,0) \in B\}$ where $A = B = T^2$

Published on 02 Mar 2020 - 20:45

score 738 · Answer 13 · 2026-03-25 16:13:58

738

Views

Can a Free product with amalgamation of $\mathbb{Z}*\mathbb{Z}$ be isomorphic to $\mathbb{Z}\times \mathbb{Z}$?

Published on 25 Mar 2026 - 16:13

score 107 · Answer 14 · 2020-03-08 09:46:43

107

Views

Attaching a $1-$cell to a space induces an injection between fundamental groups

Published on 08 Mar 2020 - 9:46

score 95 · Answer 15 · 2020-03-10 11:52:08

95

Views

What does $\pi_1(X) = 1$ mean?

Published on 10 Mar 2020 - 11:52

List Question

Proof that the edge group $E(K,v)$ of a simplicial complex is isomorphic to the fundamental group $\pi_1 (|K|,v)$ of its polyhedron.

Van Kampen Theorem proof in Hatcher's book

Manifold with infinitely many based loops but only two unbased loops (up to homotopy).

Generator of a fundamental group Algebraic Topology

Example of finite fundamental group

Isomorphism between fundamental group with end points of path as base points

Fundamental group of a space minus a point

Fundamental group of covering space given fundamental group of base

Fundamental group of a planar set: torsion free and no $\mathbb Z^2$ subgroup?

What does the notation $\pi_n(X) = 0$ and $\pi_n(X) = 1$ mean for a homotopy group?

Tammo tom Dieck's Algebraic Topology - van Kampen theorem for groupoids

Fundamental group of $(A \sqcup B)/\{A \ni (z,0) \sim (z,0) \in B\}$ where $A = B = T^2$

Can a Free product with amalgamation of $\mathbb{Z}*\mathbb{Z}$ be isomorphic to $\mathbb{Z}\times \mathbb{Z}$?

Attaching a $1-$cell to a space induces an injection between fundamental groups

What does $\pi_1(X) = 1$ mean?

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