List questions from differential-topology

Published on 14 Apr 2026 - 11:31

343

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How does degree theory imply that this mapping $f$ is locally onto?

Published on 09 Apr 2026 - 6:08

1.2k

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Tangent space to a product

Published on 12 Apr 2026 - 3:50

652

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How to check whether a vector field is Morse-Smale?

Published on 26 Mar 2026 - 12:34

149

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Conditions for a projection of a Knot to be a Knot diagram.

Published on 10 Apr 2026 - 17:20

196

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Extending metrics

Published on 09 Apr 2026 - 1:12

195

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An example of a differentiable manifold class $C^k$ but not class $C^{k +1} $

Published on 12 Apr 2026 - 13:18

106

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Existence of Solution: Embedding from 2D Euclidean space to a circle

Published on 10 Apr 2026 - 17:49

563

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Reality check: $\mathcal{O}_{\mathbb{P}_\mathbb{R}^1}(1)$ and $\mathcal{O}_{\mathbb{P}_\mathbb{R}^1}(-1)$ are both Möbius strips?

Published on 15 Apr 2026 - 0:13

368

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Example of a diffeomorphism of class $C^{k}$ which is not $C^{k+1}$

Published on 11 Apr 2026 - 12:44

3.6k

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de Rham comologies of the $n$-torus

Published on 12 Apr 2026 - 19:51

216

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Why is $\partial\partial M=\varnothing$?

Published on 09 Apr 2026 - 8:21

165

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Find an closed 1-form on $\mathbb{R}^2 \backslash (0,0)$ that is not exact.

Published on 15 Apr 2026 - 2:22

839

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Finding the degree of a map

Published on 09 Apr 2026 - 17:19

2.4k

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How to show that open interval is manifold but closed one is not

Published on 13 Apr 2026 - 6:10

List Question

Why the tangent bundle of a smooth manifold is an oriented manifold?

How does degree theory imply that this mapping $f$ is locally onto?

Tangent space to a product

How to check whether a vector field is Morse-Smale?

Conditions for a projection of a Knot to be a Knot diagram.

Extending metrics

An example of a differentiable manifold class $C^k$ but not class $C^{k +1} $

Existence of Solution: Embedding from 2D Euclidean space to a circle

Reality check: $\mathcal{O}_{\mathbb{P}_\mathbb{R}^1}(1)$ and $\mathcal{O}_{\mathbb{P}_\mathbb{R}^1}(-1)$ are both Möbius strips?

Example of a diffeomorphism of class $C^{k}$ which is not $C^{k+1}$

de Rham comologies of the $n$-torus

Why is $\partial\partial M=\varnothing$?

Find an closed 1-form on $\mathbb{R}^2 \backslash (0,0)$ that is not exact.

Finding the degree of a map

How to show that open interval is manifold but closed one is not

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