Question

Showing that $\psi^{-1}_{(x_o,g_o)}(v_1,v_2) = (\sigma_{g_o})_{s(x_o)}(s_{*x_o}(v_1)) + A^\#(s(x_o).g_o)$

score 36 · Answer 1 · 2026-03-25 12:49:43

36

Views

Showing that $\psi^{-1}_{(x_o,g_o)}(v_1,v_2) = (\sigma_{g_o})_{s(x_o)}(s_{*x_o}(v_1)) + A^\#(s(x_o).g_o)$

Published on 25 Mar 2026 - 12:49

score 909 · Answer 2 · 2017-03-29 02:11:04

909

Views

sphere bundles isomorphic to vector bundle.

Published on 29 Mar 2017 - 2:11

score 470 · Answer 3 · 2026-03-25 15:47:26

470

Views

Universal bundle over $\mathbb P^{n}$ and direct sum of bundles

Published on 25 Mar 2026 - 15:47

score 200 · Answer 4 · 2017-04-04 06:22:49

200

Views

Fiber bundles: Hairy Ball vs. $S_2\times S_1$

Published on 04 Apr 2017 - 6:22

score 155 · Answer 5 · 2026-03-25 23:37:54

155

Views

The definition of the connection on the principle bundle

Published on 25 Mar 2026 - 23:37

score 451 · Answer 6 · 2017-04-05 02:44:46

451

Views

Do flat manifolds only admit trivial bundles?

Published on 05 Apr 2017 - 2:44

score 142 · Answer 7 · 2026-03-25 23:10:10

142

Views

How to realize a smooth fibration as a subfibration of a product bundle?

Published on 25 Mar 2026 - 23:10

score 332 · Answer 8 · 2026-03-25 12:54:38

332

Views

First Chern class $c_1$ of $U(1)$ bundle over $S^2$ v.s. $\pi_1(S^1)=\mathbb{Z}$

Published on 25 Mar 2026 - 12:54

score 196 · Answer 9 · 2026-03-25 12:54:39

196

Views

Second Chern class $c_2$ of $SU(n)$ bundle over $S^4$ v.s. $\pi_3(SU(n))=\mathbb{Z}$

Published on 25 Mar 2026 - 12:54

score 83 · Answer 10 · 2023-02-07 11:15:03

83

Views

Principal bundle Isomorphism between the Hopf fibration and the orthornomal frame bundle of the tautological line bundle.

Published on 07 Feb 2023 - 11:15

score 47 · Answer 11 · 2023-02-14 07:47:16

47

Views

How is $\pi^{-1}\left(U_i\right)$ different from $U_i \times F$ in fiber bundles?

Published on 14 Feb 2023 - 7:47

score 66 · Answer 12 · 2023-02-14 11:51:46

66

Views

Is two concentric $S^1$s topologically the same as a $S^1$?

Published on 14 Feb 2023 - 11:51

score 67 · Answer 13 · 2023-02-17 13:44:55

67

Views

Notation clarification in fibre bundles

Published on 17 Feb 2023 - 13:44

score 103 · Answer 14 · 2026-03-25 12:55:02

103

Views

Classification of surface bundles and an isomorphism between $[S^n, BDiff(X)]$ and $\pi_{n-1}(Diff(X))/\pi_0(Diff(X))$

Published on 25 Mar 2026 - 12:55

score 54 · Answer 15 · 2026-03-25 17:21:30

54

Views

Are there theorems in fiber bundle land and differential geometry land that make calculations in electromagnetism easier?

Published on 25 Mar 2026 - 17:21

List Question

Showing that $\psi^{-1}_{(x_o,g_o)}(v_1,v_2) = (\sigma_{g_o})_{s(x_o)}(s_{*x_o}(v_1)) + A^\#(s(x_o).g_o)$

sphere bundles isomorphic to vector bundle.

Universal bundle over $\mathbb P^{n}$ and direct sum of bundles

Fiber bundles: Hairy Ball vs. $S_2\times S_1$

The definition of the connection on the principle bundle

Do flat manifolds only admit trivial bundles?

How to realize a smooth fibration as a subfibration of a product bundle?

First Chern class $c_1$ of $U(1)$ bundle over $S^2$ v.s. $\pi_1(S^1)=\mathbb{Z}$

Second Chern class $c_2$ of $SU(n)$ bundle over $S^4$ v.s. $\pi_3(SU(n))=\mathbb{Z}$

Principal bundle Isomorphism between the Hopf fibration and the orthornomal frame bundle of the tautological line bundle.

How is $\pi^{-1}\left(U_i\right)$ different from $U_i \times F$ in fiber bundles?

Is two concentric $S^1$s topologically the same as a $S^1$?

Notation clarification in fibre bundles

Classification of surface bundles and an isomorphism between $[S^n, BDiff(X)]$ and $\pi_{n-1}(Diff(X))/\pi_0(Diff(X))$

Are there theorems in fiber bundle land and differential geometry land that make calculations in electromagnetism easier?

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