Question

How to push up / lift a connection one-form from the base manifold to the total space?

score 172 · Answer 1 · 2023-02-23 16:08:11

172

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How to push up / lift a connection one-form from the base manifold to the total space?

Published on 23 Feb 2023 - 16:08

score 65 · Answer 2 · 2026-03-25 17:35:06

65

Views

Wilson Loops in Principal Bundle Language

Published on 25 Mar 2026 - 17:35

score 99 · Answer 3 · 2023-03-13 10:53:42

99

Views

Proof that $Aut(P) \cong H^2(X;\mathbb Z)$, where $P \to X$ is a principal $PU(\mathcal H)$-bundle.

Published on 13 Mar 2023 - 10:53

score 129 · Answer 4 · 2023-03-14 02:17:34

129

Views

Isomorphism between horizontal subspace on a principal bundle and tangent space on the base

Published on 14 Mar 2023 - 2:17

score 136 · Answer 5 · 2023-03-23 20:04:53

136

Views

Can we get a Spin-like connection from a group reduction ${\rm GL}^+(4,\mathbb{R})/{\rm Spin}^c(3,1)$ or $\exp {\rm CL}(3,1)/{\rm Spin}^c(3,1)$?

Published on 23 Mar 2023 - 20:04

score 65 · Answer 6 · 2023-04-02 19:39:54

65

Views

For every local section of a $SO(M)$ there exists precisely two local sections of $\text{Spin}(M)$

Published on 02 Apr 2023 - 19:39

score 69 · Answer 7 · 2026-03-25 19:05:04

69

Views

Existence of a principal bundle charts compatible with $f$-equivariant reductions

Published on 25 Mar 2026 - 19:05

score 71 · Answer 8 · 2023-04-13 14:47:33

71

Views

How is the connection 1 form defined?

Published on 13 Apr 2023 - 14:47

score 83 · Answer 9 · 2023-04-15 10:07:01

83

Views

Existence of smooth global orthonormal frame on a Hilbert bundle

Published on 15 Apr 2023 - 10:07

score 61 · Answer 10 · 2023-04-15 10:59:07

61

Views

Is a $Diff(M)$-invariant smooth function with a connected domain a posteriori the action by an element of $Diff(M)$?

Published on 15 Apr 2023 - 10:59

score 44 · Answer 11 · 2023-04-17 18:22:17

44

Views

Is there an elementary linear algebra mistake in Chow et al: The Ricci Flow II, appendix F about frame bundles?

Published on 17 Apr 2023 - 18:22

score 109 · Answer 12 · 2023-04-18 22:28:55

109

Views

Are normal coordinates a unique property of the Levi-Civita connection?

Published on 18 Apr 2023 - 22:28

score 21 · Answer 13 · 2023-04-19 23:55:38

21

Views

constructing principal $G$-bundles over a topological space

Published on 19 Apr 2023 - 23:55

score 190 · Answer 14 · 2023-04-21 17:33:51

190

Views

Use parallel transport to explain the homotopy lifting property

Published on 21 Apr 2023 - 17:33

score 57 · Answer 15 · 2023-04-29 19:47:43

57

Views

Bundle homomorphism is homeomorphism global from local

Published on 29 Apr 2023 - 19:47

List Question

How to push up / lift a connection one-form from the base manifold to the total space?

Wilson Loops in Principal Bundle Language

Proof that $Aut(P) \cong H^2(X;\mathbb Z)$, where $P \to X$ is a principal $PU(\mathcal H)$-bundle.

Isomorphism between horizontal subspace on a principal bundle and tangent space on the base

Can we get a Spin-like connection from a group reduction ${\rm GL}^+(4,\mathbb{R})/{\rm Spin}^c(3,1)$ or $\exp {\rm CL}(3,1)/{\rm Spin}^c(3,1)$?

For every local section of a $SO(M)$ there exists precisely two local sections of $\text{Spin}(M)$

Existence of a principal bundle charts compatible with $f$-equivariant reductions

How is the connection 1 form defined?

Existence of smooth global orthonormal frame on a Hilbert bundle

Is a $Diff(M)$-invariant smooth function with a connected domain a posteriori the action by an element of $Diff(M)$?

Is there an elementary linear algebra mistake in Chow et al: The Ricci Flow II, appendix F about frame bundles?

Are normal coordinates a unique property of the Levi-Civita connection?

constructing principal $G$-bundles over a topological space

Use parallel transport to explain the homotopy lifting property

Bundle homomorphism is homeomorphism global from local

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