List questions from vector-bundles

Published on 26 Mar 2026 - 12:58

168

Views

Understanding a trivial line subbundle of TM on the sphere

Published on 26 Mar 2026 - 6:21

142

Views

Curvature form computations

Published on 29 Mar 2026 - 20:03

66

Views

1-to-1 correspondence between pin$^−$ structure and spin structure

Published on 06 Apr 2026 - 4:55

230

Views

A contradiction involved extending vector bundles from punctured affine plane.

Published on 25 Mar 2026 - 8:07

71

Views

zero sets of fundamental vector fields

Published on 15 Dec 2020 - 1:27

141

Views

Gauge transformation (about mathematical definition of wikipedia, other sources)

Published on 26 Mar 2026 - 13:00

170

Views

Line bundles on $S^2$ and $\pi_2(\mathbb{R}P^2)$

Published on 25 Mar 2026 - 23:38

62

Views

Existence of parallel sections on pullback-bundles

Published on 29 Mar 2026 - 20:03

81

Views

Do the fiber bundles over an Abelian category form an Abelian category?

Published on 30 Mar 2026 - 15:17

445

Views

Existence of flat connections and the application of the Frobenius theorem

Published on 23 Feb 2026 - 15:18

107

Views

When can the local orientation of the sphere bundle piece together?

Published on 27 Mar 2026 - 19:15

358

Views

Realising the non-trivial orientable $S^2$-bundle over $T^2$ as a quotient of $S^2\times T^2$

Published on 30 Mar 2026 - 15:15

834

Views

Existence of specific sections of vector bundles over a manifold

Published on 25 Dec 2020 - 9:25

87

Views

Seeing explicitly what is the Euler class of the tangent bundle , $\chi(TM)=(\sum_{i=1}^n\operatorname{ind}_{p_i}X)\mu = \chi(M) \mu$

Published on 26 Mar 2026 - 6:23

List Question

Definition of odd topological K-theory using circles

Understanding a trivial line subbundle of TM on the sphere

Curvature form computations

1-to-1 correspondence between pin$^−$ structure and spin structure

A contradiction involved extending vector bundles from punctured affine plane.

zero sets of fundamental vector fields

Gauge transformation (about mathematical definition of wikipedia, other sources)

Line bundles on $S^2$ and $\pi_2(\mathbb{R}P^2)$

Existence of parallel sections on pullback-bundles

Do the fiber bundles over an Abelian category form an Abelian category?

Existence of flat connections and the application of the Frobenius theorem

When can the local orientation of the sphere bundle piece together?

Realising the non-trivial orientable $S^2$-bundle over $T^2$ as a quotient of $S^2\times T^2$

Existence of specific sections of vector bundles over a manifold

Seeing explicitly what is the Euler class of the tangent bundle , $\chi(TM)=(\sum_{i=1}^n\operatorname{ind}_{p_i}X)\mu = \chi(M) \mu$

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