List questions from differential-topology

Published on 28 Mar 2020 - 19:01

231

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'Completing' incomplete vector fields

Published on 30 Mar 2026 - 3:34

81

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What are some applications of the Morse inequalities?

Published on 25 Mar 2026 - 19:05

31

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non injective vector function

Published on 29 Mar 2020 - 3:19

217

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Piecewise smooth curve has a smooth representative

Published on 30 Mar 2026 - 3:01

639

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Does a manifold without boundary necessarily have to be the boundary of some other higher dimensional manifold?

Published on 26 Mar 2026 - 3:08

132

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Why is $f:[0,1) \rightarrow \mathbb{R}^2$ whose image is a "figure of six" a counterexample for injective immersion $\implies$ embedding?

Published on 03 Apr 2026 - 19:44

294

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Is it always possible to find a partition of unity subordinate to a cover with the same index set?

Published on 31 Mar 2020 - 12:11

216

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Projectivization of the tangent bundle to $S^2$ is nontrivial

Published on 25 Mar 2026 - 10:57

113

Views

Why does $\dim M > \dim N \implies$ there are no regular points $x \in M$, where $M,N$ are smooth manifolds?

Published on 03 Apr 2026 - 19:37

430

Views

Proof: Every point-finite open cover in a normal space has an open shrinkage

Published on 25 Mar 2026 - 22:11

364

Views

Is every loop homotopic to a smooth loop?

Published on 31 Mar 2020 - 23:20

1k

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Non-vanishing vector fields on the 2 Torus

Published on 01 Apr 2020 - 0:50

63

Views

A slightly weird topology/physics question

Published on 04 Apr 2026 - 0:55

37

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What is the map $Xf$, i.e. a section of the vector bundle apply to a smooth function on a smooth manifold $M$?

Published on 01 Apr 2020 - 18:09

List Question

Submersion and local section.

'Completing' incomplete vector fields

What are some applications of the Morse inequalities?

non injective vector function

Piecewise smooth curve has a smooth representative

Does a manifold without boundary necessarily have to be the boundary of some other higher dimensional manifold?

Why is $f:[0,1) \rightarrow \mathbb{R}^2$ whose image is a "figure of six" a counterexample for injective immersion $\implies$ embedding?

Is it always possible to find a partition of unity subordinate to a cover with the same index set?

Projectivization of the tangent bundle to $S^2$ is nontrivial

Why does $\dim M > \dim N \implies$ there are no regular points $x \in M$, where $M,N$ are smooth manifolds?

Proof: Every point-finite open cover in a normal space has an open shrinkage

Is every loop homotopic to a smooth loop?

Non-vanishing vector fields on the 2 Torus

A slightly weird topology/physics question

What is the map $Xf$, i.e. a section of the vector bundle apply to a smooth function on a smooth manifold $M$?

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