Question

Does $Ab(\pi_1(\Sigma_2)/N)=1$ imply $\pi_1(\Sigma_2)/N = 1$?

score 36 · Answer 1 · 2026-04-29 12:56:22

36

Views

Does $Ab(\pi_1(\Sigma_2)/N)=1$ imply $\pi_1(\Sigma_2)/N = 1$?

Published on 29 Apr 2026 - 12:56

score 998 · Answer 2 · 2026-04-29 12:56:17

998

Views

Prove that $\pi_1(X\times Y, (x_0,y_0))$ is isomorphic to $\pi_1(X,x_0)\times \pi_1(Y,y_0)$.

Published on 29 Apr 2026 - 12:56

score 288 · Answer 3 · 2026-04-11 17:36:34

288

Views

Induced homomorphism on $S^1$ non-trivial

Published on 11 Apr 2026 - 17:36

score 969 · Answer 4 · 2026-04-29 12:56:12

969

Views

computing the fundamental group of a wedge sum

Published on 29 Apr 2026 - 12:56

score 264 · Answer 5 · 2026-05-10 10:18:29

264

Views

Find a topological space whose fundamental group is $D_4$

Published on 10 May 2026 - 10:18

score 91 · Answer 6 · 2026-04-29 12:56:26

91

Views

Combinatorial method for fundamental group

Published on 29 Apr 2026 - 12:56

score 127 · Answer 7 · 2026-04-29 12:56:28

127

Views

Induced homomorphism of a dominating map

Published on 29 Apr 2026 - 12:56

score 950 · Answer 8 · 2026-04-29 12:56:31

950

Views

Quotient of universal cover by fundamental group

Published on 29 Apr 2026 - 12:56

score 62 · Answer 9 · 2026-04-11 01:56:35

62

Views

Possible groups for fundamental group of $\mathbb{R}$

Published on 11 Apr 2026 - 1:56

score 305 · Answer 10 · 2026-04-10 03:32:44

305

Views

Fundamental group of intersection trivial

Published on 10 Apr 2026 - 3:32

score 153 · Answer 11 · 2026-04-29 12:56:13

153

Views

Let $X$ be the space obtained from $\mathbb{R}^3$ by removing the axes $x,y$ and $z$. Calculate the fundamental group of $X$.

Published on 29 Apr 2026 - 12:56

score 63 · Answer 12 · 2026-04-29 12:56:14

63

Views

Let $Y:=\mathbb{R}^2-\{(0,1),(1,0),(-1,0)\}$. Calculate $\pi_1(Y,y_0)$, where $y_0=(0,0)$.

Published on 29 Apr 2026 - 12:56

score 534 · Answer 13 · 2026-04-15 14:18:04

534

Views

Let $A$ be a finely generated Abelian group. Prove that there is a topological space $X$ with a basic point $x_0$ such that $\pi_1(X,x_0)\cong A$.

Published on 15 Apr 2026 - 14:18

score 88 · Answer 14 · 2026-04-15 20:40:55

88

Views

Let $\mathbb{D}^3=\{(x,y,z)\in \mathbb{R}^3: x^2+y^2+z^2\leq 1\}$. Define $X=\mathbb{D}^3/\sim$ with the relation $(x,y,z)\sim(-x,-y,-z)$

Published on 15 Apr 2026 - 20:40

score 285 · Answer 15 · 2026-04-12 08:59:50

285

Views

Fundamental group S^2/~

Published on 12 Apr 2026 - 8:59

List Question

Does $Ab(\pi_1(\Sigma_2)/N)=1$ imply $\pi_1(\Sigma_2)/N = 1$?

Prove that $\pi_1(X\times Y, (x_0,y_0))$ is isomorphic to $\pi_1(X,x_0)\times \pi_1(Y,y_0)$.

Induced homomorphism on $S^1$ non-trivial

computing the fundamental group of a wedge sum

Find a topological space whose fundamental group is $D_4$

Combinatorial method for fundamental group

Induced homomorphism of a dominating map

Quotient of universal cover by fundamental group

Possible groups for fundamental group of $\mathbb{R}$

Fundamental group of intersection trivial

Let $X$ be the space obtained from $\mathbb{R}^3$ by removing the axes $x,y$ and $z$. Calculate the fundamental group of $X$.

Let $Y:=\mathbb{R}^2-\{(0,1),(1,0),(-1,0)\}$. Calculate $\pi_1(Y,y_0)$, where $y_0=(0,0)$.

Let $A$ be a finely generated Abelian group. Prove that there is a topological space $X$ with a basic point $x_0$ such that $\pi_1(X,x_0)\cong A$.

Let $\mathbb{D}^3=\{(x,y,z)\in \mathbb{R}^3: x^2+y^2+z^2\leq 1\}$. Define $X=\mathbb{D}^3/\sim$ with the relation $(x,y,z)\sim(-x,-y,-z)$

Fundamental group S^2/~

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