Question

Van Kampen's Theorem: clarification about the basepoint $x_0$

score 150 · Answer 1 · 2019-11-30 12:07:12

150

Views

Van Kampen's Theorem: clarification about the basepoint $x_0$

Published on 30 Nov 2019 - 12:07

score 777 · Answer 2 · 2019-11-30 17:20:35

777

Views

Fundamental group of mapping cone of quotient map from suspension to reduced suspension

Published on 30 Nov 2019 - 17:20

score 113 · Answer 3 · 2019-12-03 15:57:06

113

Views

Where do we use path-connectedness in the proof of van Kampen's theorem?

Published on 03 Dec 2019 - 15:57

score 410 · Answer 4 · 2026-03-26 14:35:02

410

Views

Geometric Group Theory : An application of the Švarc-Milnor lemma to Riemannian Geometry via Fundamental groups

Published on 26 Mar 2026 - 14:35

score 53 · Answer 5 · 2019-12-06 13:12:39

53

Views

What distinguishes the elements of the fundamental group of the circle?

Published on 06 Dec 2019 - 13:12

score 425 · Answer 6 · 2019-12-06 14:58:38

425

Views

Proving that the fundamental groups of two spaces with same homotopy type are isomorphic

Published on 06 Dec 2019 - 14:58

score 752 · Answer 7 · 2026-03-25 13:05:05

752

Views

Knot group is $\mathbb{Z}$ iff $K$ is the unknot

Published on 25 Mar 2026 - 13:05

score 90 · Answer 8 · 2019-12-10 02:43:35

90

Views

Fundamental group of $F_{3,0}\times S^1$

Published on 10 Dec 2019 - 2:43

score 275 · Answer 9 · 2019-12-11 10:09:29

275

Views

Calculate $\pi_{1}$ of $X = S^2 / \thicksim $ where a point on the equator is identified with its antipodal point.

Published on 11 Dec 2019 - 10:09

score 160 · Answer 10 · 2019-12-13 11:23:55

160

Views

Let $X$ be an arbitrary set equipped with the trivial topology $\{\emptyset, X\}$. Show that $\pi_1(X) = \{1\}$.

Published on 13 Dec 2019 - 11:23

score 388 · Answer 11 · 2026-03-27 05:54:40

388

Views

Covering map homeomorphism?

Published on 27 Mar 2026 - 5:54

score 241 · Answer 12 · 2019-12-14 12:34:14

241

Views

Self map of the disk: does a large degree on the boundary imply a fixed point in the interior?

Published on 14 Dec 2019 - 12:34

score 138 · Answer 13 · 2026-03-27 05:58:50

138

Views

Local path-connectedness in Theorem of Equivalent Coverings

Published on 27 Mar 2026 - 5:58

score 419 · Answer 14 · 2026-03-25 03:02:40

419

Views

$\pi_1(S^1, 1)$ via the fundamental groupoid

Published on 25 Mar 2026 - 3:02

score 349 · Answer 15 · 2019-12-18 19:34:14

349

Views

Is there a more elementary (but not trivial) example of a fundamental group than that of $S^1$?

Published on 18 Dec 2019 - 19:34

List Question

Van Kampen's Theorem: clarification about the basepoint $x_0$

Fundamental group of mapping cone of quotient map from suspension to reduced suspension

Where do we use path-connectedness in the proof of van Kampen's theorem?

Geometric Group Theory : An application of the Švarc-Milnor lemma to Riemannian Geometry via Fundamental groups

What distinguishes the elements of the fundamental group of the circle?

Proving that the fundamental groups of two spaces with same homotopy type are isomorphic

Knot group is $\mathbb{Z}$ iff $K$ is the unknot

Fundamental group of $F_{3,0}\times S^1$

Calculate $\pi_{1}$ of $X = S^2 / \thicksim $ where a point on the equator is identified with its antipodal point.

Let $X$ be an arbitrary set equipped with the trivial topology $\{\emptyset, X\}$. Show that $\pi_1(X) = \{1\}$.

Covering map homeomorphism?

Self map of the disk: does a large degree on the boundary imply a fixed point in the interior?

Local path-connectedness in Theorem of Equivalent Coverings

$\pi_1(S^1, 1)$ via the fundamental groupoid

Is there a more elementary (but not trivial) example of a fundamental group than that of $S^1$?

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