Question

Role of path connectedness in fundamental group of product space

score 552 · Answer 1 · 2026-03-25 09:50:05

552

Views

Role of path connectedness in fundamental group of product space

Published on 25 Mar 2026 - 9:50

score 28 · Answer 2 · 2018-06-16 19:15:35

28

Views

Instability of even windings of SO(4)

Published on 16 Jun 2018 - 19:15

score 264 · Answer 3 · 2018-06-23 09:20:03

264

Views

Two points from the same topological space that their fundamental group is not isomorphic.

Published on 23 Jun 2018 - 9:20

score 206 · Answer 4 · 2018-06-28 15:45:25

206

Views

Fundamental group of $\mathbb{R}^3 \setminus \{ \mathbb{S}^1 \text{ and two lines} \}$

Published on 28 Jun 2018 - 15:45

score 737 · Answer 5 · 2018-07-01 08:12:41

737

Views

Prove that $f:X\to S^1$ is null-homotopic iff homomorphism $f_*:\pi_1(X,x)\to\pi_1(S^1,f(x))$ is trivial for some $x$.

Published on 01 Jul 2018 - 8:12

score 339 · Answer 6 · 2018-07-02 11:49:22

339

Views

Find fundamental group of space $X=(S^1\times S^1)/(S^1\times \{s_0\})$

Published on 02 Jul 2018 - 11:49

score 1.5k · Answer 7 · 2018-07-02 19:16:28

1.5k

Views

If $A$ is a deformation retract of $X$ and $B$ is a deformation retract of $A$ then $ B$ is a deforemation retract of X

Published on 02 Jul 2018 - 19:16

score 1.5k · Answer 8 · 2026-03-25 12:53:43

1.5k

Views

Covering spaces of $\mathbb{C}^{\times}$

Published on 25 Mar 2026 - 12:53

score 467 · Answer 9 · 2018-07-08 10:45:21

467

Views

Homology group of $\mathbb{S}^1 \vee \mathbb{RP}^2$ and covering spaces

Published on 08 Jul 2018 - 10:45

score 202 · Answer 10 · 2018-07-09 10:55:34

202

Views

Covering spaces of $\mathbb{T} \times \mathbb{RP}^2$

Published on 09 Jul 2018 - 10:55

score 418 · Answer 11 · 2026-03-22 17:38:22

418

Views

Equivalence of Categories between the Fundamental Group and Groupoid

Published on 22 Mar 2026 - 17:38

score 200 · Answer 12 · 2018-07-11 08:16:50

200

Views

How to build homotopy from convex to a point?

Published on 11 Jul 2018 - 8:16

score 70 · Answer 13 · 2018-07-11 23:11:18

70

Views

Why is $N(p_(\pi_1(T, \overline{x}_0)))/p_\pi_1(X, x_0) \cong D$?

Published on 11 Jul 2018 - 23:11

score 954 · Answer 14 · 2026-03-25 12:55:41

954

Views

Deck transformation group isomorphic to $\mathbb{Z}/\mathbb{6Z}$

Published on 25 Mar 2026 - 12:55

score 50 · Answer 15 · 2018-07-13 12:25:08

50

Views

What does n times a generator of a cyclic group mean?

Published on 13 Jul 2018 - 12:25

List Question

Role of path connectedness in fundamental group of product space

Instability of even windings of SO(4)

Two points from the same topological space that their fundamental group is not isomorphic.

Fundamental group of $\mathbb{R}^3 \setminus \{ \mathbb{S}^1 \text{ and two lines} \}$

Prove that $f:X\to S^1$ is null-homotopic iff homomorphism $f_*:\pi_1(X,x)\to\pi_1(S^1,f(x))$ is trivial for some $x$.

Find fundamental group of space $X=(S^1\times S^1)/(S^1\times \{s_0\})$

If $A$ is a deformation retract of $X$ and $B$ is a deformation retract of $A$ then $ B$ is a deforemation retract of X

Covering spaces of $\mathbb{C}^{\times}$

Homology group of $\mathbb{S}^1 \vee \mathbb{RP}^2$ and covering spaces

Covering spaces of $\mathbb{T} \times \mathbb{RP}^2$

Equivalence of Categories between the Fundamental Group and Groupoid

How to build homotopy from convex to a point?

Why is $N(p_(\pi_1(T, \overline{x}_0)))/p_\pi_1(X, x_0) \cong D$?

Deck transformation group isomorphic to $\mathbb{Z}/\mathbb{6Z}$

What does n times a generator of a cyclic group mean?

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