List questions from differential-topology

Published on 15 Apr 2026 - 19:03

279

Views

What is the smoothness of a family of diffeomorphisms $t\mapsto \psi_t \in \text{Diff}(M)$ ? And how to interpret it intuitively?

Published on 29 Mar 2026 - 20:56

163

Views

Proving that every tangent bundle is direct summand of a trivial bundle.

Published on 27 Apr 2026 - 15:04

598

Views

Definition of a cubic coordinate system

Published on 13 Apr 2026 - 12:35

2.7k

Views

Why does a tangent bundle have dimension 2n instead of n?

Published on 15 Apr 2026 - 4:14

440

Views

Exact sequences of bundles and orientations

Published on 16 Apr 2026 - 17:19

302

Views

Extending a section to a basis of sections in a trivial bundle.

Published on 27 Apr 2026 - 4:50

53

Views

Vector fields- differential topology

Published on 17 Apr 2026 - 12:39

1.2k

Views

For any smooth manifold, is it true that for any two points on the manifold, there exists a chart that covers the two points?

Published on 15 Apr 2026 - 17:20

203

Views

Non-homotopical manifolds with same de Rham cohomology

Published on 14 Apr 2026 - 4:13

515

Views

Is $n$-dim manifold which is immersed in $\mathbb{R}^n$ diffeomorphic to a ball?

Published on 15 Apr 2026 - 21:14

69

Views

Is this map an immersion?

Published on 11 Apr 2026 - 7:32

1k

Views

Avoiding the spherical polar coordinate singularity on $S^2$ by using a double cover?

Published on 13 Apr 2026 - 22:19

677

Views

What is the moment of inertia tensor of a hollow spheroid?

Published on 16 Apr 2026 - 14:45

137

Views

What is the index of a vector field with positive divergence?

Published on 13 Apr 2026 - 20:20

List Question

Transition maps on Grassmanian $Gr(2,5)$

What is the smoothness of a family of diffeomorphisms $t\mapsto \psi_t \in \text{Diff}(M)$ ? And how to interpret it intuitively?

Proving that every tangent bundle is direct summand of a trivial bundle.

Definition of a cubic coordinate system

Why does a tangent bundle have dimension 2n instead of n?

Exact sequences of bundles and orientations

Extending a section to a basis of sections in a trivial bundle.

Vector fields- differential topology

For any smooth manifold, is it true that for any two points on the manifold, there exists a chart that covers the two points?

Non-homotopical manifolds with same de Rham cohomology

Is $n$-dim manifold which is immersed in $\mathbb{R}^n$ diffeomorphic to a ball?

Is this map an immersion?

Avoiding the spherical polar coordinate singularity on $S^2$ by using a double cover?

What is the moment of inertia tensor of a hollow spheroid?

What is the index of a vector field with positive divergence?

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