List questions from differential-topology

56

Views

Showing the inverse of $f: S^{n-1} \to S^{n-1}$ defined by $f(x) = \frac{e \cdot x}{\|e \cdot x\|}$ is smooth.

Published on 01 Oct 2016 - 1:37

164

Views

A division algebra on $\mathbb{R}^n$ implies $S^{n-1}$ is parallelizable.

Published on 01 Oct 2016 - 4:37

130

Views

If $M_g$ is a genus $0$ surface, why are there no nonseparating curves?

Published on 29 Mar 2026 - 12:41

281

Views

How can I prove that a circle is the only compact connected 1-manifold?

Published on 01 Oct 2016 - 11:47

1.6k

Views

Intuition behind the Thom Isomorphism.

Published on 26 Mar 2026 - 6:20

76

Views

How to show that every compact 2-manifold, which is complex, is differentiable manifold?

Published on 01 Oct 2016 - 15:28

514

Views

illustrative book of differential geometry

Published on 01 Oct 2016 - 17:51

108

Views

Diffeomorphism between $n$-fold and $m$-fold tori

Published on 01 Oct 2016 - 20:49

116

Views

Showing transversality more rigorously.

Published on 25 Mar 2026 - 11:09

213

Views

Property of non-transversal manifold

Published on 01 Oct 2016 - 23:46

2k

Views

When is a smooth homeomorphism a diffeomorphism?

Published on 02 Oct 2016 - 14:40

44

Views

Why should we consider $\sqrt{b/a}$ instead of $\frac{b}{a}$?

Published on 02 Oct 2016 - 22:00

674

Views

Clarification as to why $O(n)$ is closed?

Published on 03 Oct 2016 - 0:47

294

Views

Morse Theory and Electrostatic Problem: Why a finite number of critical points?

Published on 25 Mar 2026 - 23:37

116

Views

Determine whether diffeomorphism is also a symplectomorphism

Published on 27 Mar 2026 - 23:01

List Question

Showing the inverse of $f: S^{n-1} \to S^{n-1}$ defined by $f(x) = \frac{e \cdot x}{\|e \cdot x\|}$ is smooth.

A division algebra on $\mathbb{R}^n$ implies $S^{n-1}$ is parallelizable.

If $M_g$ is a genus $0$ surface, why are there no nonseparating curves?

How can I prove that a circle is the only compact connected 1-manifold?

Intuition behind the Thom Isomorphism.

How to show that every compact 2-manifold, which is complex, is differentiable manifold?

illustrative book of differential geometry

Diffeomorphism between $n$-fold and $m$-fold tori

Showing transversality more rigorously.

Property of non-transversal manifold

When is a smooth homeomorphism a diffeomorphism?

Why should we consider $\sqrt{b/a}$ instead of $\frac{b}{a}$?

Clarification as to why $O(n)$ is closed?

Morse Theory and Electrostatic Problem: Why a finite number of critical points?

Determine whether diffeomorphism is also a symplectomorphism

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