List questions from differential-topology

Published on 11 Apr 2026 - 8:05

487

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How to show $\dim T_x(X) = \dim df_x T_x(X).$

Published on 16 Apr 2026 - 5:16

194

Views

Does "Add up" just means oriented counterclockwisely?

Published on 12 Apr 2026 - 9:49

238

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Calculate $\deg(f)$

Published on 16 Apr 2026 - 10:51

152

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Prove $G = \left\{ \mathrm{diag} (e^{ti}, e^{\lambda ti}) \mid t \in \mathbb{R} \right\}$ is not a manifold.

Published on 13 Apr 2026 - 18:12

120

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Prove $z \to z^m$ has degree $m$.

Published on 15 Apr 2026 - 1:01

105

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Proof that $\operatorname{rank}(dT)=1$ implies the image is a curve

Published on 15 Apr 2026 - 18:00

625

Views

What do we mean when we say a differential form "descends to the quotient"?

Published on 16 Apr 2026 - 22:08

586

Views

Inner product of De Rham cohomology classes

Published on 14 Apr 2026 - 1:19

74

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Why not extending to the whole disk implies have a zero

Published on 14 Apr 2026 - 7:22

76

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Why the degree of $p/|p|$ is zero on $\partial W^\prime?$

Published on 14 Apr 2026 - 12:39

269

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Plus or minus? Is there a canonical orientation, like counterclockwisely?

Published on 15 Apr 2026 - 18:46

55

Views

Prove $I(Z,X) = -I(X,Z)$.

Published on 16 Apr 2026 - 13:07

88

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$T: \mathbb{R}^n\to \mathbb{R}^m$, $n>m$, $\operatorname{rank}(dT)=m$, show $T$ maps open sets to open sets.

Published on 16 Apr 2026 - 4:34

481

Views

On framed manifolds

Published on 11 Apr 2026 - 20:06

List Question

How does one define mixed partial derivatives for functions on a manifold?

How to show $\dim T_x(X) = \dim df_x T_x(X).$

Does "Add up" just means oriented counterclockwisely?

Calculate $\deg(f)$

Prove $G = \left\{ \mathrm{diag} (e^{ti}, e^{\lambda ti}) \mid t \in \mathbb{R} \right\}$ is not a manifold.

Prove $z \to z^m$ has degree $m$.

Proof that $\operatorname{rank}(dT)=1$ implies the image is a curve

What do we mean when we say a differential form "descends to the quotient"?

Inner product of De Rham cohomology classes

Why not extending to the whole disk implies have a zero

Why the degree of $p/|p|$ is zero on $\partial W^\prime?$

Plus or minus? Is there a canonical orientation, like counterclockwisely?

Prove $I(Z,X) = -I(X,Z)$.

$T: \mathbb{R}^n\to \mathbb{R}^m$, $n>m$, $\operatorname{rank}(dT)=m$, show $T$ maps open sets to open sets.

On framed manifolds

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