Question

Is the special orthogonal group really rationally homotopy commutative?

score 488 · Answer 1 · 2026-03-29 05:35:12

488

Views

Is the special orthogonal group really rationally homotopy commutative?

Published on 29 Mar 2026 - 5:35

score 773 · Answer 2 · 2026-03-26 01:11:35

773

Views

Compute directly that the mapping cone of a homotopy equivalence is contractible

Published on 26 Mar 2026 - 1:11

score 55 · Answer 3 · 2016-03-19 03:00:02

55

Views

Homotopy of induced homomorphism

Published on 19 Mar 2016 - 3:00

score 50 · Answer 4 · 2016-03-19 12:31:59

50

Views

Showing $\bar{p} * \alpha * p \simeq_{x_0} \bar{p} * \beta * p$, path-homotopy

Published on 19 Mar 2016 - 12:31

score 610 · Answer 5 · 2016-03-21 05:42:04

610

Views

$X$ is contractible if and only if $X \simeq \{ * \} $ - A three-part question

Published on 21 Mar 2016 - 5:42

score 5.9k · Answer 6 · 2016-03-21 12:44:17

5.9k

Views

Show that a contractible space is simply connected

Published on 21 Mar 2016 - 12:44

score 210 · Answer 7 · 2026-05-11 07:22:50

210

Views

Can we always find homotopy of two paths which lies "between" the paths?

Published on 11 May 2026 - 7:22

score 87 · Answer 8 · 2016-03-24 18:46:46

87

Views

Homotopy of boundary paths

Published on 24 Mar 2016 - 18:46

score 4.1k · Answer 9 · 2016-03-25 11:41:51

4.1k

Views

A space is contractible if and only if its identity map is nullhomotopic

Published on 25 Mar 2016 - 11:41

score 50 · Answer 10 · 2016-03-27 13:48:02

50

Views

Proving homotopy of 2 paths

Published on 27 Mar 2016 - 13:48

score 26 · Answer 11 · 2016-03-27 19:56:38

26

Views

Prove |[X,Z]| = |[Y,Z]| where X, Y are homotopic and Z is a top space

Published on 27 Mar 2016 - 19:56

score 121 · Answer 12 · 2026-05-10 18:27:56

121

Views

Equivalence of $[X,K(\mathbb{Z},n)]$ and $\langle X,K(\mathbb{Z},n)\rangle$ when $X$ is a CW complex but not connected

Published on 10 May 2026 - 18:27

score 47 · Answer 13 · 2016-03-30 04:11:06

47

Views

Let $\omega_n: I \to S^1$ by $\omega_n(t)=\exp (2\pi int)$. Show that $\omega_p * \omega_q$ is homotopic, rel endpoints, to $\omega_{p+q}$.

Published on 30 Mar 2016 - 4:11

score 2.7k · Answer 14 · 2016-03-30 12:03:13

2.7k

Views

Examples of Same fundamental group but not homeomorphic

Published on 30 Mar 2016 - 12:03

score 691 · Answer 15 · 2016-03-30 12:28:49

691

Views

Homotopy equivalence of a space with the sphere

Published on 30 Mar 2016 - 12:28

List Question

Is the special orthogonal group really rationally homotopy commutative?

Compute directly that the mapping cone of a homotopy equivalence is contractible

Homotopy of induced homomorphism

Showing $\bar{p} * \alpha * p \simeq_{x_0} \bar{p} * \beta * p$, path-homotopy

$X$ is contractible if and only if $X \simeq \{ * \} $ - A three-part question

Show that a contractible space is simply connected

Can we always find homotopy of two paths which lies "between" the paths?

Homotopy of boundary paths

A space is contractible if and only if its identity map is nullhomotopic

Proving homotopy of 2 paths

Prove |[X,Z]| = |[Y,Z]| where X, Y are homotopic and Z is a top space

Equivalence of $[X,K(\mathbb{Z},n)]$ and $\langle X,K(\mathbb{Z},n)\rangle$ when $X$ is a CW complex but not connected

Let $\omega_n: I \to S^1$ by $\omega_n(t)=\exp (2\pi int)$. Show that $\omega_p * \omega_q$ is homotopic, rel endpoints, to $\omega_{p+q}$.

Examples of Same fundamental group but not homeomorphic

Homotopy equivalence of a space with the sphere

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