List questions from fiber-bundles

Published on 02 May 2022 - 17:17

115

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What is a symplectic structure on a smooth vector bundle

Published on 06 May 2022 - 18:18

78

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homogeneous circle bundle over a hyperbolic surface

Published on 06 May 2022 - 22:33

40

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Why is for cotangent bundles $T^X_1 \times T^X_2 \simeq T^*(X_1 \times X_2)$

Published on 07 May 2022 - 19:40

159

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Convexity in "usual Partition of Unity arguments"

Published on 19 May 2022 - 1:23

41

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Do unique horizontal lifts of path homotopic paths through a point are always path homotopic?

Published on 28 Mar 2026 - 16:17

278

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Definition of static spherically symmetric spacetime as fiber bundle

Published on 29 Mar 2026 - 7:39

46

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Smooth $S^1$-bundle over complex projective line

Published on 31 May 2022 - 22:10

222

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Fibers of a locally trivial fibration are diffeomorphic

Published on 29 Mar 2026 - 10:08

53

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Definition of fiber not given in map $\text{Spec }\mathbb{C}[x,y,t] / \langle xy-t \rangle \to \text{Spec } \mathbb{C}[t].$

Published on 07 Jun 2022 - 19:55

117

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Is My Understanding of Covariant Derivative Right?

Published on 30 Mar 2026 - 20:42

72

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$\mathbb{C}P^2$ as a $U(1)$ bundle

Published on 28 Mar 2026 - 16:12

63

Views

For a trivial fiber G-bundle transition functions $t_{UV}: U \cap V \to G$ can be defined as $t_{UV}(x) = f_U(x)f_V^{-1}(x)$, for continuous $f_U,f_V$

Published on 10 Jun 2022 - 11:08

94

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Is the space $\mathbb{PR}^3$ homeomorphic to $\mathbb{PR}^2\times S^1$?

Published on 02 Apr 2026 - 18:47

105

Views

How to build an Atlas on the total space in bundle reconstruction

Published on 28 Mar 2026 - 16:14

List Question

The total space of the standard quaternionic Hopf fibration of an $S^3$ fiber bundle over $S^4.$

What is a symplectic structure on a smooth vector bundle

homogeneous circle bundle over a hyperbolic surface

Why is for cotangent bundles $T^X_1 \times T^X_2 \simeq T^*(X_1 \times X_2)$

Convexity in "usual Partition of Unity arguments"

Do unique horizontal lifts of path homotopic paths through a point are always path homotopic?

Definition of static spherically symmetric spacetime as fiber bundle

Smooth $S^1$-bundle over complex projective line

Fibers of a locally trivial fibration are diffeomorphic

Definition of fiber not given in map $\text{Spec }\mathbb{C}[x,y,t] / \langle xy-t \rangle \to \text{Spec } \mathbb{C}[t].$

Is My Understanding of Covariant Derivative Right?

$\mathbb{C}P^2$ as a $U(1)$ bundle

For a trivial fiber G-bundle transition functions $t_{UV}: U \cap V \to G$ can be defined as $t_{UV}(x) = f_U(x)f_V^{-1}(x)$, for continuous $f_U,f_V$

Is the space $\mathbb{PR}^3$ homeomorphic to $\mathbb{PR}^2\times S^1$?

How to build an Atlas on the total space in bundle reconstruction

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