Question

Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

score 821 · Answer 1 · 2026-03-20 07:55:44

821

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Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

Published on 20 Mar 2026 - 7:55

score 68 · Answer 2 · 2026-03-22 13:15:10

68

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$f$ has square root if and only if image of $f_*$ contained in $2 \mathbb Z$

Published on 22 Mar 2026 - 13:15

score 58 · Answer 3 · 2026-03-20 06:26:36

58

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Homotopic maps between pointed sets induce same group homomorphism

Published on 20 Mar 2026 - 6:26

score 42 · Answer 4 · 2026-03-20 00:06:55

42

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If $H \le \pi_1(X,x)$ is conjugate to $P_(\pi_1(Y, y))$, then $H \cong P_(\pi_1(Y, y'))$ for some $y' \in P^{-1}(x)$

Published on 20 Mar 2026 - 0:06

score 415 · Answer 5 · 2026-03-22 04:00:55

415

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Calculating the fundamental group of $S^1$ with SvK

Published on 22 Mar 2026 - 4:00

score 1.6k · Answer 6 · 2026-03-20 01:34:15

1.6k

Views

Monodromy representation.

Published on 20 Mar 2026 - 1:34

score 46 · Answer 7 · 2026-03-20 01:32:18

46

Views

A set of generators of $\pi_1(X,x_0)$ where $X=U\cup V$ and $U\cap V$ path connected

Published on 20 Mar 2026 - 1:32

score 85 · Answer 8 · 2026-03-20 11:49:21

85

Views

Is the fundamental group of the image a subgroup of the fundamental group of the domain?

Published on 20 Mar 2026 - 11:49

score 134 · Answer 9 · 2026-03-22 05:09:25

134

Views

Showing that $\pi_1(X/G) \cong G$.

Published on 22 Mar 2026 - 5:09

score 401 · Answer 10 · 2026-03-22 06:11:34

401

Views

Fundamental group of a mapping cone

Published on 22 Mar 2026 - 6:11

score 853 · Answer 11 · 2026-03-22 14:40:22

853

Views

Is there a subset of $\mathbb R^2$ that has fundamental group $\mathbb Z^2$?

Published on 22 Mar 2026 - 14:40

score 1.3k · Answer 12 · 2026-03-25 07:25:47

1.3k

Views

Representation of fundamental group and flat bundle

Published on 25 Mar 2026 - 7:25

score 237 · Answer 13 · 2026-03-25 06:21:04

237

Views

Manifolds covered by finitely many charts

Published on 25 Mar 2026 - 6:21

score 67 · Answer 14 · 2026-03-17 08:34:26

67

Views

Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

Published on 17 Mar 2026 - 8:34

score 903 · Answer 15 · 2026-03-25 06:24:51

903

Views

Show that the fundamental group of wedge of two circles is non Abelian without actually computing it.

Published on 25 Mar 2026 - 6:24

List Question

Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

$f$ has square root if and only if image of $f_*$ contained in $2 \mathbb Z$

Homotopic maps between pointed sets induce same group homomorphism

If $H \le \pi_1(X,x)$ is conjugate to $P_(\pi_1(Y, y))$, then $H \cong P_(\pi_1(Y, y'))$ for some $y' \in P^{-1}(x)$

Calculating the fundamental group of $S^1$ with SvK

Monodromy representation.

A set of generators of $\pi_1(X,x_0)$ where $X=U\cup V$ and $U\cap V$ path connected

Is the fundamental group of the image a subgroup of the fundamental group of the domain?

Showing that $\pi_1(X/G) \cong G$.

Fundamental group of a mapping cone

Is there a subset of $\mathbb R^2$ that has fundamental group $\mathbb Z^2$?

Representation of fundamental group and flat bundle

Manifolds covered by finitely many charts

Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

Show that the fundamental group of wedge of two circles is non Abelian without actually computing it.

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