List questions from differential-topology

Published on 14 May 2026 - 16:02

614

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If $M\subset\mathbb{R}^n$ is a submanifold of dimension $d<m$ then $M$ has measure zero.

Published on 15 Apr 2026 - 6:16

83

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Sum of Dolbeault cohomology and homotopy invariance

Published on 14 Apr 2026 - 0:15

258

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Show that for a properly embedded submanifold the manifold and topogoical boundary coincide

Published on 13 Apr 2026 - 13:46

829

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If $\partial\Omega$ is of class $C^1$, does it need to be the boundary of a $C^1$-regular domain?

Published on 17 Apr 2026 - 1:56

1k

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On the equivalence of several definitions of the torus

Published on 13 Apr 2026 - 18:55

268

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Does the pushforward of a smooth map on a manifold coincide with the derivative in a tangent direction of any local extension?

Published on 11 May 2026 - 5:33

1.1k

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Deforming the torus without a point to $S^1 \lor S^1$

Published on 14 Apr 2026 - 7:21

132

Views

Determining the tangent space of a submanifold of $\Bbb C^3$

Published on 14 Apr 2026 - 22:04

79

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Strategy for proving a set is the fiber of a (possible) fiber bundle $p: E\to B$

Published on 11 May 2026 - 7:52

257

Views

How to imagine/prove that all of the following pictures are 2-torus?

Published on 16 Apr 2026 - 0:13

35

Views

If $T_t$ is a family of diffeomorphisms on $U$ and $V_2⊆U$ is open, is there an open set $V_1⊆U$ with $T_t(V_1)⊆V_2$ for $t$ sufficiently small?

Published on 13 Apr 2026 - 2:01

127

Views

Why does simple counter-example to global inverse theorem not work?

Published on 17 Apr 2026 - 6:44

228

Views

Different perspectives on smoothing theory

Published on 10 Apr 2026 - 11:32

99

Views

Explicit example of recovering a manifold from its group of homeomorphisms

Published on 11 Apr 2026 - 8:35

List Question

Definition of the tangential gradient

If $M\subset\mathbb{R}^n$ is a submanifold of dimension $d<m$ then $M$ has measure zero.

Sum of Dolbeault cohomology and homotopy invariance

Show that for a properly embedded submanifold the manifold and topogoical boundary coincide

If $\partial\Omega$ is of class $C^1$, does it need to be the boundary of a $C^1$-regular domain?

On the equivalence of several definitions of the torus

Does the pushforward of a smooth map on a manifold coincide with the derivative in a tangent direction of any local extension?

Deforming the torus without a point to $S^1 \lor S^1$

Determining the tangent space of a submanifold of $\Bbb C^3$

Strategy for proving a set is the fiber of a (possible) fiber bundle $p: E\to B$

How to imagine/prove that all of the following pictures are 2-torus?

If $T_t$ is a family of diffeomorphisms on $U$ and $V_2⊆U$ is open, is there an open set $V_1⊆U$ with $T_t(V_1)⊆V_2$ for $t$ sufficiently small?

Why does simple counter-example to global inverse theorem not work?

Different perspectives on smoothing theory

Explicit example of recovering a manifold from its group of homeomorphisms

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