Question

how to calculate the fundamental group using van kampen theorem?

score 307 · Answer 1 · 2018-04-20 13:51:48

307

Views

how to calculate the fundamental group using van kampen theorem?

Published on 20 Apr 2018 - 13:51

score 525 · Answer 2 · 2026-03-23 02:41:36

525

Views

How to define an action of $\pi_1(E)$ on $\pi_n(F)$ for a fibration $F\to E\to B$?

Published on 23 Mar 2026 - 2:41

score 223 · Answer 3 · 2026-03-25 07:45:02

223

Views

Why is no covering space of $\mathbb{R}P^2 \vee S^1$ homeomorphic to an orientable surface?

Published on 25 Mar 2026 - 7:45

score 88 · Answer 4 · 2018-04-22 20:42:47

88

Views

Show that there are exactly two spaces obtained from identifying edges of a triangle.

Published on 22 Apr 2018 - 20:42

score 182 · Answer 5 · 2018-04-23 06:28:59

182

Views

Are spaces $X, Y$ with $\pi_{1}(X) \cong \pi_{1}(Y)$, $\widetilde{X} \simeq \widetilde{Y}$ necessarily homotopy equivalent?

Published on 23 Apr 2018 - 6:28

score 566 · Answer 6 · 2026-03-25 07:42:57

566

Views

Topological structure of the dunce hat

Published on 25 Mar 2026 - 7:42

score 1.6k · Answer 7 · 2026-03-22 18:21:16

1.6k

Views

Find a space whose fundamental group is $\mathbb Z/2 × \mathbb Z$

Published on 22 Mar 2026 - 18:21

score 265 · Answer 8 · 2026-03-25 00:04:25

265

Views

Find the fundamental group of (Z × Z) ∗ Z and (Z ∗ Z) × Z

Published on 25 Mar 2026 - 0:04

score 72 · Answer 9 · 2026-03-25 09:43:12

72

Views

Let $K$ be the Klein bottle. Give examples of cover spaces $p_1:E_1\to K, p_1:E_2\to K$ each with two sheets and such that $E_1$ and $E_2$

Published on 25 Mar 2026 - 9:43

score 70 · Answer 10 · 2026-03-25 09:39:42

70

Views

Classify, except isomorphism, all the associated covering spaces of $3$ sheets on $\mathbb{S}^1\times\mathbb{S}^1$. Do the same for the

Published on 25 Mar 2026 - 9:39

score 1.1k · Answer 11 · 2026-03-25 09:38:47

1.1k

Views

Find the universal covering of $\mathbb{R}P^2\vee\mathbb{R}P^2$

Published on 25 Mar 2026 - 9:38

score 232 · Answer 12 · 2026-03-25 09:43:11

232

Views

Show that if $X$ is homotopically equivalent to $Y$, then $\widetilde{X}$ is homotopically equivalent to $\widetilde{Y}$

Published on 25 Mar 2026 - 9:43

score 169 · Answer 13 · 2026-03-25 09:35:41

169

Views

Let $p: E\rightarrow B$ and $p':E' \rightarrow B$ covering map, E and E' path-connected and locally path-connected, isomorphismus between E and E'

Published on 25 Mar 2026 - 9:35

score 107 · Answer 14 · 2018-05-07 14:36:24

107

Views

Fundamental Group of $GL_r(\mathbb{C})$

Published on 07 May 2018 - 14:36

score 416 · Answer 15 · 2018-05-11 01:41:32

416

Views

Show that $\pi_1 ( \mathbb{R}^2 - \mathbb{Q}^2)$ is uncountable

Published on 11 May 2018 - 1:41

List Question

how to calculate the fundamental group using van kampen theorem?

How to define an action of $\pi_1(E)$ on $\pi_n(F)$ for a fibration $F\to E\to B$?

Why is no covering space of $\mathbb{R}P^2 \vee S^1$ homeomorphic to an orientable surface?

Show that there are exactly two spaces obtained from identifying edges of a triangle.

Are spaces $X, Y$ with $\pi_{1}(X) \cong \pi_{1}(Y)$, $\widetilde{X} \simeq \widetilde{Y}$ necessarily homotopy equivalent?

Topological structure of the dunce hat

Find a space whose fundamental group is $\mathbb Z/2 × \mathbb Z$

Find the fundamental group of (Z × Z) ∗ Z and (Z ∗ Z) × Z

Let $K$ be the Klein bottle. Give examples of cover spaces $p_1:E_1\to K, p_1:E_2\to K$ each with two sheets and such that $E_1$ and $E_2$

Classify, except isomorphism, all the associated covering spaces of $3$ sheets on $\mathbb{S}^1\times\mathbb{S}^1$. Do the same for the

Find the universal covering of $\mathbb{R}P^2\vee\mathbb{R}P^2$

Show that if $X$ is homotopically equivalent to $Y$, then $\widetilde{X}$ is homotopically equivalent to $\widetilde{Y}$

Let $p: E\rightarrow B$ and $p':E' \rightarrow B$ covering map, E and E' path-connected and locally path-connected, isomorphismus between E and E'

Fundamental Group of $GL_r(\mathbb{C})$

Show that $\pi_1 ( \mathbb{R}^2 - \mathbb{Q}^2)$ is uncountable

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