Question

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

score 102 · Answer 1 · 2026-04-02 23:32:39

102

Views

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

Published on 02 Apr 2026 - 23:32

score 56 · Answer 2 · 2026-03-26 02:53:08

56

Views

Chern forms and tensor products

Published on 26 Mar 2026 - 2:53

score 38 · Answer 3 · 2022-05-06 09:02:35

38

Views

Why can extensions of a section of a vector bundle over a finite number of trivializing sets glue together?

Published on 06 May 2022 - 9:02

score 116 · Answer 4 · 2026-04-02 23:33:32

116

Views

What is a symplectic structure on a smooth vector bundle

Published on 02 Apr 2026 - 23:33

score 74 · Answer 5 · 2026-03-30 17:00:54

74

Views

Exterior covariant derivative for a bundle-valued $n$-form for a connection without torsion

Published on 30 Mar 2026 - 17:00

score 41 · Answer 6 · 2026-04-02 23:35:24

41

Views

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

Published on 02 Apr 2026 - 23:35

score 332 · Answer 7 · 2022-05-09 16:58:11

332

Views

Splitting of short exact sequence of holomorphic vector bundle

Published on 09 May 2022 - 16:58

score 100 · Answer 8 · 2026-03-28 09:56:48

100

Views

Does a non-trivial orientable vector bundle with rank $n$ have $n$ independent sections?

Published on 28 Mar 2026 - 9:56

score 91 · Answer 9 · 2026-03-28 18:16:48

91

Views

The $n$-th Stiefel–Whitney class $w_n \ne 0$ indicates that every section of the vector bundle (rank $n$) must vanish at some point

Published on 28 Mar 2026 - 18:16

score 56 · Answer 10 · 2022-05-11 21:41:23

A non-orientable vector bundle (rank $n$), for any collection of sections {$s_1, …,s_n$}, at least one subset of $E_b$ is zero? $s_i(b)=0$

score 238 · Answer 11 · 2026-03-28 18:16:59

238

Views

The isomorphism $H^1(X;\mathbb Z_2) \rightarrow \operatorname{Hom}(\pi_1(X),\mathbb Z_2)$ and $w_1(E)$

Published on 28 Mar 2026 - 18:16

score 87 · Answer 12 · 2022-05-12 17:22:22

87

Views

Does a covering by trivializations imply existence of a linearly compatible one, for a smooth $\mathbb{R}^k$ fiber bundle?

Published on 12 May 2022 - 17:22

score 61 · Answer 13 · 2022-05-14 14:05:00

61

Views

Husemoller: homotopy of linear clutching map (proposition $4.5$, pag. $187$)

Published on 14 May 2022 - 14:05

score 170 · Answer 14 · 2026-03-27 08:42:03

170

Views

Rank of a coherent sheaf using resolution by vector bundles

Published on 27 Mar 2026 - 8:42

score 114 · Answer 15 · 2022-05-16 10:17:09

114

Views

Is the Lagrangian canonical momentum the fiber derivative of the Lagrangian?

Published on 16 May 2022 - 10:17

List Question

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

Chern forms and tensor products

Why can extensions of a section of a vector bundle over a finite number of trivializing sets glue together?

What is a symplectic structure on a smooth vector bundle

Exterior covariant derivative for a bundle-valued $n$-form for a connection without torsion

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

Splitting of short exact sequence of holomorphic vector bundle

Does a non-trivial orientable vector bundle with rank $n$ have $n$ independent sections?

The $n$-th Stiefel–Whitney class $w_n \ne 0$ indicates that every section of the vector bundle (rank $n$) must vanish at some point

A non-orientable vector bundle (rank $n$), for any collection of sections {$s_1, …,s_n$}, at least one subset of $E_b$ is zero? $s_i(b)=0$

The isomorphism $H^1(X;\mathbb Z_2) \rightarrow \operatorname{Hom}(\pi_1(X),\mathbb Z_2)$ and $w_1(E)$

Does a covering by trivializations imply existence of a linearly compatible one, for a smooth $\mathbb{R}^k$ fiber bundle?

Husemoller: homotopy of linear clutching map (proposition $4.5$, pag. $187$)

Rank of a coherent sheaf using resolution by vector bundles

Is the Lagrangian canonical momentum the fiber derivative of the Lagrangian?

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