List questions from differential-topology

Published on 09 Apr 2026 - 13:06

117

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Can we form a topological or Banach space of $C^1$-differentiable functions on a manifold?

Published on 11 May 2026 - 8:39

104

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Closed embedding of the half line in a non-compact manifold

Published on 12 Apr 2026 - 19:34

216

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Retraction, inclusion and homotopy

Published on 13 Apr 2026 - 15:04

53

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Smooth functions defined on connected sums

Published on 11 May 2026 - 6:12

65

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Square Roots of Diffeomorhpisms of Manifold Conjugate?

Published on 13 Apr 2026 - 13:59

88

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Have I really proved Exercise 23.5 in Tu's Manifolds, or how to amend this proof?

Published on 17 Apr 2026 - 22:22

134

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Milnor, Lectures on the h-cobordism theorem, proof of Theorem 3.4

Published on 14 Apr 2026 - 18:35

593

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Notion of degree of a map from an orientable manifold to non-orientable manifold

Published on 15 Apr 2026 - 1:08

88

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Component function of the differential of a curve in a local frame

Published on 15 Apr 2026 - 10:13

54

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$C^r$ sections can be approximated by $C^s$ sections

Published on 15 Apr 2026 - 6:20

50

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Parametrize 1-Manifold?

Published on 16 Apr 2026 - 8:18

70

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Given $f:\mathbb{R}^m \supset U \rightarrow \mathbb{R}^n$ differential. Relation of rank of $f'$ and the property of image of $f$?

Published on 16 Apr 2026 - 21:20

99

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Convergence of vectors in the tangent bundle after an embedding implies convergence at the source

Published on 14 Apr 2026 - 16:22

311

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Some examples and non-examples of topological manifolds (w boundary or not)

Published on 14 Apr 2026 - 2:07

List Question

How do we need to apply the fundamental theorem of homomorphisms here?

Can we form a topological or Banach space of $C^1$-differentiable functions on a manifold?

Closed embedding of the half line in a non-compact manifold

Retraction, inclusion and homotopy

Smooth functions defined on connected sums

Square Roots of Diffeomorhpisms of Manifold Conjugate?

Have I really proved Exercise 23.5 in Tu's Manifolds, or how to amend this proof?

Milnor, Lectures on the h-cobordism theorem, proof of Theorem 3.4

Notion of degree of a map from an orientable manifold to non-orientable manifold

Component function of the differential of a curve in a local frame

$C^r$ sections can be approximated by $C^s$ sections

Parametrize 1-Manifold?

Given $f:\mathbb{R}^m \supset U \rightarrow \mathbb{R}^n$ differential. Relation of rank of $f'$ and the property of image of $f$?

Convergence of vectors in the tangent bundle after an embedding implies convergence at the source

Some examples and non-examples of topological manifolds (w boundary or not)

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