List questions from differential-topology

Published on 02 Feb 2018 - 16:36

29

Views

Studying the differentiability of $f(P) = P(0)P'(1)$

Published on 03 Feb 2018 - 12:43

270

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if $df_x$ is an isomorphism, why is $f$ locally equivalent to the identity?

Published on 04 Feb 2018 - 22:24

602

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Confusion about Local Coordinates

Published on 04 Feb 2018 - 22:41

755

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Different definitions of derivation at a point

Published on 17 Mar 2026 - 4:59

130

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generators for the mapping class group of a neighborhood of curves?

Published on 17 Mar 2026 - 19:29

90

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Is there always a positive projection map from a generic open subset of $\mathbb{R}^n$ to $\mathbb{R}$?

Published on 25 Mar 2026 - 1:17

539

Views

Show the diagonal $\Delta \subseteq X\times X$ is diffeomorphic to $X$, so $\Delta$ is a manifold if $X$ is

Published on 22 Mar 2026 - 15:30

69

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Problem on Independent Functions

Published on 07 Feb 2018 - 17:03

384

Views

Show that the map $p$ is a submersion except at finitely many points.

Published on 08 Feb 2018 - 0:01

1.2k

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Is a smooth injective map an immersion?

Published on 08 Feb 2018 - 10:26

621

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Is there a function $f\colon \Bbb R\to \Bbb R$ with uncountably many critical values?

Published on 09 Feb 2018 - 2:38

382

Views

If integrals of pullbacks of a form only depend on the boundary values, is it exact?

Published on 17 Mar 2026 - 10:48

245

Views

Spherical triangle has the sum of interior angles greater than 180

Published on 16 Mar 2026 - 22:26

330

Views

The Converse of Poincare Lemma

Published on 22 Mar 2026 - 18:46

List Question

connected 2D manifold contained in a 2D affine plane

Studying the differentiability of $f(P) = P(0)P'(1)$

if $df_x$ is an isomorphism, why is $f$ locally equivalent to the identity?

Confusion about Local Coordinates

Different definitions of derivation at a point

generators for the mapping class group of a neighborhood of curves?

Is there always a positive projection map from a generic open subset of $\mathbb{R}^n$ to $\mathbb{R}$?

Show the diagonal $\Delta \subseteq X\times X$ is diffeomorphic to $X$, so $\Delta$ is a manifold if $X$ is

Problem on Independent Functions

Show that the map $p$ is a submersion except at finitely many points.

Is a smooth injective map an immersion?

Is there a function $f\colon \Bbb R\to \Bbb R$ with uncountably many critical values?

If integrals of pullbacks of a form only depend on the boundary values, is it exact?

Spherical triangle has the sum of interior angles greater than 180

The Converse of Poincare Lemma

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