Question

Intuitive visualization or understanding from $S^2$ to $SO(3)$ and $S^3$ -- and where to find an $S^1$?

score 79 · Answer 1 · 2021-03-30 16:59:51

79

Views

Intuitive visualization or understanding from $S^2$ to $SO(3)$ and $S^3$ -- and where to find an $S^1$?

Published on 30 Mar 2021 - 16:59

score 235 · Answer 2 · 2021-04-03 15:18:21

235

Views

Visualizing $\mathbb{S}^{3}$ as consisting of two "polar" great circles together with a family of nested Clifford tori interpolating between them.

Published on 03 Apr 2021 - 15:18

score 1000 · Answer 3 · 2021-04-07 07:26:00

1000

Views

Proving that the Hopf map $S^3 \to S^2$ is a submersion

Published on 07 Apr 2021 - 7:26

score 202 · Answer 4 · 2026-03-25 12:27:25

202

Views

How to show that higher Hopf fibrations are not nullhomotopic?

Published on 25 Mar 2026 - 12:27

score 1.2k · Answer 5 · 2021-05-18 05:59:40

1.2k

Views

Proving that the Hopf Fibration is a fiber bundle

Published on 18 May 2021 - 5:59

score 150 · Answer 6 · 2021-05-25 13:41:30

150

Views

Computation of vertical vectors of the Hopf fibration $S^1 \hookrightarrow S^3 \rightarrow S^2$

Published on 25 May 2021 - 13:41

score 1.2k · Answer 7 · 2021-06-24 19:06:54

1.2k

Views

How does the Hopf fibration generalize to maps $S^{2n+1}\to \mathbb{CP}^n$?

Published on 24 Jun 2021 - 19:06

score 252 · Answer 8 · 2021-08-05 02:59:02

252

Views

Inverting the Hopf map from $\mathbb{CP}^1$ to $\mathbb{S}^2$

Published on 05 Aug 2021 - 2:59

score 332 · Answer 9 · 2021-08-11 01:36:38

332

Views

Hopf fibration from Hopf link: change to a different ambient space or a different type of link

Published on 11 Aug 2021 - 1:36

score 276 · Answer 10 · 2021-09-25 20:51:52

276

Views

Connecting the quaternion formulation with the complex line through the hypersphere in Hopf's fibrations.

Published on 25 Sep 2021 - 20:51

score 121 · Answer 11 · 2021-10-26 22:41:31

121

Views

How to prove that a map is a Hurewicz fibration?

Published on 26 Oct 2021 - 22:41

score 196 · Answer 12 · 2022-01-10 15:59:56

196

Views

Hopf fibration from $SO(3)$ Lie algebra generators?

Published on 10 Jan 2022 - 15:59

score 75 · Answer 13 · 2022-01-25 20:50:08

75

Views

Help with closing this novel proof of the equivalence of oriented Grassmannians $G^+(2, 4)$ and $S^2\times S^2$

Published on 25 Jan 2022 - 20:50

score 189 · Answer 14 · 2022-02-02 22:49:03

189

Views

Trivialisation of the Hopf bundle

Published on 02 Feb 2022 - 22:49

score 137 · Answer 15 · 2022-02-14 14:14:36

137

Views

Fundamental Group of Complement to Several Hopf Circles

Published on 14 Feb 2022 - 14:14

List Question

Intuitive visualization or understanding from $S^2$ to $SO(3)$ and $S^3$ -- and where to find an $S^1$?

Visualizing $\mathbb{S}^{3}$ as consisting of two "polar" great circles together with a family of nested Clifford tori interpolating between them.

Proving that the Hopf map $S^3 \to S^2$ is a submersion

How to show that higher Hopf fibrations are not nullhomotopic?

Proving that the Hopf Fibration is a fiber bundle

Computation of vertical vectors of the Hopf fibration $S^1 \hookrightarrow S^3 \rightarrow S^2$

How does the Hopf fibration generalize to maps $S^{2n+1}\to \mathbb{CP}^n$?

Inverting the Hopf map from $\mathbb{CP}^1$ to $\mathbb{S}^2$

Hopf fibration from Hopf link: change to a different ambient space or a different type of link

Connecting the quaternion formulation with the complex line through the hypersphere in Hopf's fibrations.

How to prove that a map is a Hurewicz fibration?

Hopf fibration from $SO(3)$ Lie algebra generators?

Help with closing this novel proof of the equivalence of oriented Grassmannians $G^+(2, 4)$ and $S^2\times S^2$

Trivialisation of the Hopf bundle

Fundamental Group of Complement to Several Hopf Circles

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