Question

Degree of universal cover of simple Lie group

score 75 · Answer 1 · 2026-03-25 23:39:32

75

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Degree of universal cover of simple Lie group

Published on 25 Mar 2026 - 23:39

score 265 · Answer 2 · 2026-03-25 22:05:10

265

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The fundamental group of the Lattice - (R x Z) U (Z x R)

Published on 25 Mar 2026 - 22:05

score 1.3k · Answer 3 · 2026-03-25 09:33:14

1.3k

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Hatcher Exercise 1.2.8

Published on 25 Mar 2026 - 9:33

score 58 · Answer 4 · 2019-01-29 10:58:58

58

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find two topological spaces $Y_1$, $Y_2$ such that $\pi (Y_1)=\pi (Y_2)= (0)$ but $\pi (Y_1 \cup Y_2)\ne (0)$

Published on 29 Jan 2019 - 10:58

score 934 · Answer 5 · 2019-01-30 12:37:39

934

Views

How is going around the circle once in each direction homotopic to a point?

Published on 30 Jan 2019 - 12:37

score 335 · Answer 6 · 2019-02-03 13:28:07

335

Views

Fundamental group of uncountable space with cofinite topology

Published on 03 Feb 2019 - 13:28

score 144 · Answer 7 · 2019-02-11 08:49:39

144

Views

Surjectivity of sending loop from fundamental group to the endpoint of its lift?

Published on 11 Feb 2019 - 8:49

score 505 · Answer 8 · 2026-03-25 09:29:58

505

Views

Let $X$ be a connected CW complex and $G$ a group such that every $\pi_1(X)\to G$ is trivial. Show that every $X\to K(G, 1)$ is nullhomotopic.

Published on 25 Mar 2026 - 9:29

score 97 · Answer 9 · 2019-02-12 17:15:28

97

Views

Finding an open simply connected subset in a punctured open simply connected set

Published on 12 Feb 2019 - 17:15

score 72 · Answer 10 · 2026-03-26 02:56:24

72

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If $f_0=\omega_m$ and $f_1=\omega_n$, why is it not automatic that $\tilde f_0 = \tilde \omega_m$ and $\tilde f_1 = \tilde \omega_n$?

Published on 26 Mar 2026 - 2:56

score 818 · Answer 11 · 2019-02-13 19:53:19

818

Views

Loops as maps from $S^1\to X$, Hatcher 1.15

Published on 13 Feb 2019 - 19:53

score 71 · Answer 12 · 2019-02-14 08:40:12

71

Views

First fundamental group and connectedness of $X:=\mathbb{R^4}\setminus \{\pi_1 \cup \pi_2 \}$

Published on 14 Feb 2019 - 8:40

score 230 · Answer 13 · 2019-02-14 14:31:19

230

Views

Hatcher Lemma 1.19

Published on 14 Feb 2019 - 14:31

score 682 · Answer 14 · 2019-02-16 13:50:19

682

Views

What can we say about two topological spaces with the same fundamental group?

Published on 16 Feb 2019 - 13:50

score 40 · Answer 15 · 2019-02-17 13:06:14

40

Views

Fundametal group and continuous extension to $\Bbb R^n$

Published on 17 Feb 2019 - 13:06

List Question

Degree of universal cover of simple Lie group

The fundamental group of the Lattice - (R x Z) U (Z x R)

Hatcher Exercise 1.2.8

find two topological spaces $Y_1$, $Y_2$ such that $\pi (Y_1)=\pi (Y_2)= (0)$ but $\pi (Y_1 \cup Y_2)\ne (0)$

How is going around the circle once in each direction homotopic to a point?

Fundamental group of uncountable space with cofinite topology

Surjectivity of sending loop from fundamental group to the endpoint of its lift?

Let $X$ be a connected CW complex and $G$ a group such that every $\pi_1(X)\to G$ is trivial. Show that every $X\to K(G, 1)$ is nullhomotopic.

Finding an open simply connected subset in a punctured open simply connected set

If $f_0=\omega_m$ and $f_1=\omega_n$, why is it not automatic that $\tilde f_0 = \tilde \omega_m$ and $\tilde f_1 = \tilde \omega_n$?

Loops as maps from $S^1\to X$, Hatcher 1.15

First fundamental group and connectedness of $X:=\mathbb{R^4}\setminus \{\pi_1 \cup \pi_2 \}$

Hatcher Lemma 1.19

What can we say about two topological spaces with the same fundamental group?

Fundametal group and continuous extension to $\Bbb R^n$

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