List questions from differential-topology

Published on 11 Apr 2026 - 6:26

124

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Connection between (1,1) tensors and maps of vector fields

Published on 11 Feb 2024 - 18:12

105

Views

Naive linear algebra in vector bundles

Published on 01 Apr 2026 - 11:15

93

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Prove that if every smooth function on a subset of a manifold can be extended to a smooth function on the whole manifold, then the subset is closed.

Published on 28 Mar 2026 - 15:36

37

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B-Isomorphic? (Husemoller, Fiber Bundles). Illustrated diagrams included.

Published on 27 Mar 2026 - 22:52

52

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Guillemin's proof of manifold boundary dimension

Published on 26 Mar 2026 - 23:11

144

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Understanding $\mathbb{C}P^2$

Published on 01 Apr 2026 - 5:34

62

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$z \mapsto z^m$ is orientation preserving and regular

Published on 12 Apr 2026 - 0:59

43

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Is the image of the projection of a smooth curve onto a subset of its coordinates a manifold if the projection is an injective immersion?

Published on 13 Apr 2026 - 12:13

39

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Calculate the differentiate of $ Q: \mathbb{R}^n \rightarrow \mathbb{R}$ defined by $Q(x)=B(x;x)$

Published on 30 Mar 2026 - 3:38

63

Views

Why are coordinate maps diffeomorphisms (revisited)

Published on 13 Apr 2026 - 10:54

33

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Conditions for the implicit function theorem being satisfied giving rise to $n-1$ dimensional manifold

Published on 13 Apr 2026 - 13:41

74

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Tangent vector of vector space

Published on 26 Mar 2026 - 19:38

82

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Orientability issue when classifying symplectic structures on compact orientable surfaces

Published on 09 Apr 2026 - 8:48

63

Views

There exist holomorphic maps from a torus $T$ to the sphere $S$ of all degree $\geq 2$

Published on 13 Apr 2026 - 6:03

List Question

Explicit connection between vector fields and derivations

Connection between (1,1) tensors and maps of vector fields

Naive linear algebra in vector bundles

Prove that if every smooth function on a subset of a manifold can be extended to a smooth function on the whole manifold, then the subset is closed.

B-Isomorphic? (Husemoller, Fiber Bundles). Illustrated diagrams included.

Guillemin's proof of manifold boundary dimension

Understanding $\mathbb{C}P^2$

$z \mapsto z^m$ is orientation preserving and regular

Is the image of the projection of a smooth curve onto a subset of its coordinates a manifold if the projection is an injective immersion?

Calculate the differentiate of $ Q: \mathbb{R}^n \rightarrow \mathbb{R}$ defined by $Q(x)=B(x;x)$

Why are coordinate maps diffeomorphisms (revisited)

Conditions for the implicit function theorem being satisfied giving rise to $n-1$ dimensional manifold

Tangent vector of vector space

Orientability issue when classifying symplectic structures on compact orientable surfaces

There exist holomorphic maps from a torus $T$ to the sphere $S$ of all degree $\geq 2$

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