List questions from manifolds

Published on 15 Apr 2026 - 19:17

190

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Let $M$ and $N$ be smooth manifolds and $f: M\rightarrow N$ a diffeomorphism. Prove that the map $df:TM \rightarrow TN$ is a homeomorphism.

Published on 29 Apr 2026 - 6:41

1.2k

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About the definition of tangent space of smooth manifold

Published on 10 Apr 2026 - 4:54

1k

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Gradient of a functional

Published on 05 May 2026 - 10:01

384

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Doubt about $n$-holed Torus and Handles

Published on 11 Apr 2026 - 4:15

442

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Lemme 2.4 in Morse theory by Milnor

Published on 26 Mar 2026 - 12:41

484

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Sobolev trace theorem for manifolds with boundary

Published on 19 Apr 2026 - 21:31

165

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Definition of a submanifold

Published on 24 Apr 2026 - 19:20

1.4k

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Uniqueness of Smoothed Corners

Published on 29 Apr 2026 - 6:39

933

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Smooth Structure of the Torus

Published on 10 Apr 2026 - 19:16

158

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The zero set of $z_0^2+z_1^2-1$ in $\mathbb{C}^2$.

Published on 17 Apr 2026 - 12:37

472

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Finding the kernel of Pushforward of $f:\mathbb R^n\rightarrow \mathbb R^k$

Published on 29 Apr 2026 - 6:40

3.1k

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Orthogonal group is a regular submanifold of $GL(n,\Bbb R)$

Published on 13 Apr 2026 - 15:41

1.7k

Views

Constant Rank theorem for domain with nonempty boundary

Published on 14 Apr 2026 - 4:58

131

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Show the regular submanifold

Published on 14 Apr 2026 - 11:33

List Question

Why functions $f_{\alpha \beta} \colon U_\alpha \cap U_\beta \to Y$ are called cocycles?

Let $M$ and $N$ be smooth manifolds and $f: M\rightarrow N$ a diffeomorphism. Prove that the map $df:TM \rightarrow TN$ is a homeomorphism.

About the definition of tangent space of smooth manifold

Gradient of a functional

Doubt about $n$-holed Torus and Handles

Lemme 2.4 in Morse theory by Milnor

Sobolev trace theorem for manifolds with boundary

Definition of a submanifold

Uniqueness of Smoothed Corners

Smooth Structure of the Torus

The zero set of $z_0^2+z_1^2-1$ in $\mathbb{C}^2$.

Finding the kernel of Pushforward of $f:\mathbb R^n\rightarrow \mathbb R^k$

Orthogonal group is a regular submanifold of $GL(n,\Bbb R)$

Constant Rank theorem for domain with nonempty boundary

Show the regular submanifold

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