Question

Isomorphism of vector bundles $T\mathbb{C}P^2\cong \operatorname{Hom}(E,E^\perp)$, and matching up their transition functions.

score 86 · Answer 1 · 2018-06-03 10:52:44

86

Views

Isomorphism of vector bundles $T\mathbb{C}P^2\cong \operatorname{Hom}(E,E^\perp)$, and matching up their transition functions.

Published on 03 Jun 2018 - 10:52

score 783 · Answer 2 · 2026-03-25 12:29:31

783

Views

Is the tangent bundle of a $S^2$ flat?

Published on 25 Mar 2026 - 12:29

score 44 · Answer 3 · 2026-03-22 17:45:50

44

Views

Let $M$ be a complex manifold. Why are the bundles $\bigwedge^{p, q}M$ not holomorphic vector bundles over $M$ for $q \neq 0$ ?

Published on 22 Mar 2026 - 17:45

score 140 · Answer 4 · 2026-03-23 03:37:48

140

Views

Is $\bigwedge^{p,0}M$ a holomorphic vector bundle?

Published on 23 Mar 2026 - 3:37

score 236 · Answer 5 · 2018-06-05 15:38:21

236

Views

Composition of vector bundles is only a fibre bundle

Published on 05 Jun 2018 - 15:38

score 225 · Answer 6 · 2026-03-25 07:40:46

225

Views

curvature of vector bundle

Published on 25 Mar 2026 - 7:40

score 491 · Answer 7 · 2026-03-25 07:41:44

491

Views

Square root of even degree line bundle

Published on 25 Mar 2026 - 7:41

score 356 · Answer 8 · 2018-06-11 18:46:05

356

Views

Can we continuously choose a basis for the kernel of a continuously family of matrices of constant rank over $\mathbb C$?

Published on 11 Jun 2018 - 18:46

score 182 · Answer 9 · 2018-06-16 04:35:13

182

Views

Local coordinates of a vector field; derivative wrt 1-forms

Published on 16 Jun 2018 - 4:35

score 147 · Answer 10 · 2026-03-25 12:27:08

147

Views

About the antisymmetry of the curvature matrix in vector bundle

Published on 25 Mar 2026 - 12:27

score 447 · Answer 11 · 2026-03-25 03:22:15

447

Views

Proof of the formula for the exterior derivative in terms of the covariant derivative.

Published on 25 Mar 2026 - 3:22

score 105 · Answer 12 · 2018-06-22 12:30:21

105

Views

Some properties vector bundles and Thom spaces

Published on 22 Jun 2018 - 12:30

score 49 · Answer 13 · 2026-03-25 07:47:55

49

Views

The proof of $c_1(E)\in \tilde{H}^2(X,\mathbb{Z})$ when $E\to X$ is a complex line bundle.

Published on 25 Mar 2026 - 7:47

score 144 · Answer 14 · 2018-06-26 01:57:31

144

Views

2-dimensional vector bundles on projective 3-space

Published on 26 Jun 2018 - 1:57

score 1k · Answer 15 · 2018-06-27 13:12:31

1k

Views

Horizontal and vertical bundles

Published on 27 Jun 2018 - 13:12

List Question

Isomorphism of vector bundles $T\mathbb{C}P^2\cong \operatorname{Hom}(E,E^\perp)$, and matching up their transition functions.

Is the tangent bundle of a $S^2$ flat?

Let $M$ be a complex manifold. Why are the bundles $\bigwedge^{p, q}M$ not holomorphic vector bundles over $M$ for $q \neq 0$ ?

Is $\bigwedge^{p,0}M$ a holomorphic vector bundle?

Composition of vector bundles is only a fibre bundle

curvature of vector bundle

Square root of even degree line bundle

Can we continuously choose a basis for the kernel of a continuously family of matrices of constant rank over $\mathbb C$?

Local coordinates of a vector field; derivative wrt 1-forms

About the antisymmetry of the curvature matrix in vector bundle

Proof of the formula for the exterior derivative in terms of the covariant derivative.

Some properties vector bundles and Thom spaces

The proof of $c_1(E)\in \tilde{H}^2(X,\mathbb{Z})$ when $E\to X$ is a complex line bundle.

2-dimensional vector bundles on projective 3-space

Horizontal and vertical bundles

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