List questions from differential-topology

Published on 18 Apr 2026 - 2:03

105

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Change of Coordinates - John Lee's Smooth Manifolds, eq. 3.11

Published on 14 Apr 2026 - 23:19

95

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Explicit example of Integral de Rham cohomology

Published on 12 Apr 2026 - 8:44

86

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How to proof that a manifold covered by two charts satisfying $f_i(\mathbb{R}^m \setminus B^o) \subset f_j(B^o)$ for $i\not=j$ is simply connected?

Published on 15 Apr 2026 - 19:35

569

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Verification that a map between product manifolds is smooth

Published on 12 Apr 2026 - 6:42

75

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Explicit expression $\int_{M} Tr(R \wedge R )$ in terms of Riemann tensor with coordinate indices

Published on 11 Apr 2026 - 22:31

122

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diffeomorphic closed manifolds are cobordant

Published on 08 Apr 2026 - 17:25

118

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Milnor's notation for tangent bundle

Published on 14 Apr 2026 - 12:38

203

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Submanifold of Orientable Manifold with Codimension 0 is Orientable

Published on 12 Apr 2026 - 4:13

104

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Reference request: sheaf cohomology after Bott & Tu

Published on 17 Apr 2026 - 0:37

61

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Global Frobenius Theorem- Warner's Proof(Theorem 1.64, Page 48-49)

Published on 11 Apr 2026 - 11:20

142

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Why "compactness" assumption in the statement that $S$ is not boundary of some oriented compact smooth submanifold is necessary?

Published on 18 Apr 2026 - 7:48

55

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Equality in definition of topology via open sets and neighborhood

Published on 13 Apr 2026 - 19:57

149

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Interpretation of Integral of Differential 3-Form over 3-Manifold in Engineering?

Published on 14 Apr 2026 - 16:13

188

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Poincaré group as a topology and a Lie group manifold

Published on 16 Apr 2026 - 13:57

List Question

Notation Understanding Difficulty

Change of Coordinates - John Lee's Smooth Manifolds, eq. 3.11

Explicit example of Integral de Rham cohomology

How to proof that a manifold covered by two charts satisfying $f_i(\mathbb{R}^m \setminus B^o) \subset f_j(B^o)$ for $i\not=j$ is simply connected?

Verification that a map between product manifolds is smooth

Explicit expression $\int_{M} Tr(R \wedge R )$ in terms of Riemann tensor with coordinate indices

diffeomorphic closed manifolds are cobordant

Milnor's notation for tangent bundle

Submanifold of Orientable Manifold with Codimension 0 is Orientable

Reference request: sheaf cohomology after Bott & Tu

Global Frobenius Theorem- Warner's Proof(Theorem 1.64, Page 48-49)

Why "compactness" assumption in the statement that $S$ is not boundary of some oriented compact smooth submanifold is necessary?

Equality in definition of topology via open sets and neighborhood

Interpretation of Integral of Differential 3-Form over 3-Manifold in Engineering?

Poincaré group as a topology and a Lie group manifold

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