Question

Strategy for proving a set is the fiber of a (possible) fiber bundle $p: E\to B$

score 78 · Answer 1 · 2026-03-25 16:03:34

78

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Strategy for proving a set is the fiber of a (possible) fiber bundle $p: E\to B$

Published on 25 Mar 2026 - 16:03

score 1.4k · Answer 2 · 2026-03-27 21:36:29

1.4k

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Fundamental group of the total space of an oriented $S^1$ fiber bundle over $T^2$

Published on 27 Mar 2026 - 21:36

score 88 · Answer 3 · 2026-03-27 19:53:22

88

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Notational confusion regarding textbook exercise ("Differential Geometry" by Loring Tu)

Published on 27 Mar 2026 - 19:53

score 84 · Answer 4 · 2020-08-22 13:14:34

84

Views

For a covering space $p:\tilde{X}\to X$, there is a bijection $p^{-1}(x_0)\to p^{-1}(x_1)$, for $x_0,x_1\in X$

Published on 22 Aug 2020 - 13:14

score 214 · Answer 5 · 2026-03-27 19:54:10

214

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How do I prove that the typical fibre of the associated bundle $(P_F:=(P\times F)/\sim_G,\pi_F,M)$ is $F$?

Published on 27 Mar 2026 - 19:54

score 233 · Answer 6 · 2026-03-27 19:51:43

233

Views

Principal bundle over an associated bundle

Published on 27 Mar 2026 - 19:51

score 126 · Answer 7 · 2020-08-29 11:22:29

126

Views

Understanding fiber bundles over manifolds of finite type (finite good cover)

Published on 29 Aug 2020 - 11:22

score 144 · Answer 8 · 2026-03-27 19:52:44

144

Views

Decomposition of a connection on a principal bundle

Published on 27 Mar 2026 - 19:52

score 106 · Answer 9 · 2020-09-09 13:48:39

106

Views

Checking whether a map between the fibre of an associated bundle $(P_F:=(P\times F)/\sim_G,\pi_F,M)$ and F is well-defined

Published on 09 Sep 2020 - 13:48

score 379 · Answer 10 · 2026-02-23 12:27:42

379

Views

Non zero sections of sheaves which vanish on all fibers

Published on 23 Feb 2026 - 12:27

score 240 · Answer 11 · 2026-03-27 21:37:23

240

Views

What is the (oriented) orthonormal frame bundle of $(S^{3}\times S^{1})$?

Published on 27 Mar 2026 - 21:37

score 97 · Answer 12 · 2026-03-26 04:34:34

97

Views

Why are equivalent "a connection form is reducible" and "a connection generated by the connection form preserves a metric"?

Published on 26 Mar 2026 - 4:34

score 74 · Answer 13 · 2020-09-23 19:51:05

74

Views

Simple example of a fiber bundle.

Published on 23 Sep 2020 - 19:51

score 109 · Answer 14 · 2026-03-27 21:37:23

109

Views

Connections on principal and associated fiber bundles exercises

Published on 27 Mar 2026 - 21:37

score 84 · Answer 15 · 2026-03-29 03:10:54

84

Views

Describe $\mathcal{N}_{G(\mathbb{P}^1,\mathbb{P}^k)\mid G(\mathbb{P}^1,\mathbb{P}^n)}$

Published on 29 Mar 2026 - 3:10

List Question

Strategy for proving a set is the fiber of a (possible) fiber bundle $p: E\to B$

Fundamental group of the total space of an oriented $S^1$ fiber bundle over $T^2$

Notational confusion regarding textbook exercise ("Differential Geometry" by Loring Tu)

For a covering space $p:\tilde{X}\to X$, there is a bijection $p^{-1}(x_0)\to p^{-1}(x_1)$, for $x_0,x_1\in X$

How do I prove that the typical fibre of the associated bundle $(P_F:=(P\times F)/\sim_G,\pi_F,M)$ is $F$?

Principal bundle over an associated bundle

Understanding fiber bundles over manifolds of finite type (finite good cover)

Decomposition of a connection on a principal bundle

Checking whether a map between the fibre of an associated bundle $(P_F:=(P\times F)/\sim_G,\pi_F,M)$ and F is well-defined

Non zero sections of sheaves which vanish on all fibers

What is the (oriented) orthonormal frame bundle of $(S^{3}\times S^{1})$?

Why are equivalent "a connection form is reducible" and "a connection generated by the connection form preserves a metric"?

Simple example of a fiber bundle.

Connections on principal and associated fiber bundles exercises

Describe $\mathcal{N}_{G(\mathbb{P}^1,\mathbb{P}^k)\mid G(\mathbb{P}^1,\mathbb{P}^n)}$

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