Question

The module of section of a vector bundle and the module of section of the pullbackbundle are isomorphic

score 25 · Answer 1 · 2026-04-04 23:01:34

25

Views

The module of section of a vector bundle and the module of section of the pullbackbundle are isomorphic

Published on 04 Apr 2026 - 23:01

score 34 · Answer 2 · 2026-04-02 21:47:31

34

Views

Let $(E,B,\pi)$ be vector bundle and $W \subseteq E$. Prove $W = \pi^{-1}(W \cap B)$.

Published on 02 Apr 2026 - 21:47

score 152 · Answer 3 · 2026-04-01 01:30:21

152

Views

Splitting Lemma for Vector Bundles

Published on 01 Apr 2026 - 1:30

score 117 · Answer 4 · 2026-03-26 14:19:49

117

Views

Adjoint of a end-valued complex differential form

Published on 26 Mar 2026 - 14:19

score 52 · Answer 5 · 2022-04-26 19:47:08

52

Views

Isomorphism in the space of section of a trivial vector bundle

Published on 26 Apr 2022 - 19:47

score 161 · Answer 6 · 2026-03-26 04:31:25

161

Views

How does the Borel-Weil theorem works? What do we use it for, how does the application look generally?

Published on 26 Mar 2026 - 4:31

score 222 · Answer 7 · 2026-04-02 21:49:21

222

Views

correspondence between local section and local trivalization for vector bundle and principle $G$-bundle

Published on 02 Apr 2026 - 21:49

score 139 · Answer 8 · 2026-03-28 14:44:35

139

Views

Hermitian metrics on the Associated Vector Bundle of a Principal $U(1)$-bundle

Published on 28 Mar 2026 - 14:44

score 196 · Answer 9 · 2026-03-26 04:34:01

196

Views

The first Stiefel-Whitney class of a trivial line bundle $E=M \times \mathbb{R}$

Published on 26 Mar 2026 - 4:34

score 217 · Answer 10 · 2026-03-26 02:58:27

217

Views

Normal bundle of a non-orientable manifold

Published on 26 Mar 2026 - 2:58

score 263 · Answer 11 · 2026-03-25 22:05:15

263

Views

Why the fiber of the normal bundle of the Klein bottle is $\mathbb{R}^2$ instead of $\mathbb{R}$?

Published on 25 Mar 2026 - 22:05

score 182 · Answer 12 · 2026-03-28 20:22:21

182

Views

Prove the non-orientability of a vector bundle using the first Stiefel-Whitney class $w_1 \neq 0$

Published on 28 Mar 2026 - 20:22

score 72 · Answer 13 · 2026-03-26 14:23:08

72

Views

Is $TM\oplus NM \cong M\times \mathbb{R}^n $ valid if the manifold $M$ is immersed in $\mathbb{R^n}$?

Published on 26 Mar 2026 - 14:23

score 63 · Answer 14 · 2026-04-02 21:51:52

63

Views

Understanding the transition map in the case of the proof that $S^3$ bundles over $S^4$

Published on 02 Apr 2026 - 21:51

score 63 · Answer 15 · 2026-03-28 20:14:54

63

Views

If the first Stiefel-Whitney class of a subset $\gamma$ of a vector bundle $E$ is $w_1(\gamma)\neq 0$, is $w_1(E)\neq 0$ as well?

Published on 28 Mar 2026 - 20:14

List Question

The module of section of a vector bundle and the module of section of the pullbackbundle are isomorphic

Let $(E,B,\pi)$ be vector bundle and $W \subseteq E$. Prove $W = \pi^{-1}(W \cap B)$.

Splitting Lemma for Vector Bundles

Adjoint of a end-valued complex differential form

Isomorphism in the space of section of a trivial vector bundle

How does the Borel-Weil theorem works? What do we use it for, how does the application look generally?

correspondence between local section and local trivalization for vector bundle and principle $G$-bundle

Hermitian metrics on the Associated Vector Bundle of a Principal $U(1)$-bundle

The first Stiefel-Whitney class of a trivial line bundle $E=M \times \mathbb{R}$

Normal bundle of a non-orientable manifold

Why the fiber of the normal bundle of the Klein bottle is $\mathbb{R}^2$ instead of $\mathbb{R}$?

Prove the non-orientability of a vector bundle using the first Stiefel-Whitney class $w_1 \neq 0$

Is $TM\oplus NM \cong M\times \mathbb{R}^n $ valid if the manifold $M$ is immersed in $\mathbb{R^n}$?

Understanding the transition map in the case of the proof that $S^3$ bundles over $S^4$

If the first Stiefel-Whitney class of a subset $\gamma$ of a vector bundle $E$ is $w_1(\gamma)\neq 0$, is $w_1(E)\neq 0$ as well?

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