List questions from differential-topology

Published on 13 Apr 2026 - 15:12

157

Views

Perelman's theorem in dimensions other than 3 (and 4) - why is it "easy"?

Published on 13 Apr 2026 - 12:52

147

Views

$\chi(A\cup B)=\chi(A)+\chi(B)-\chi(A\cap B)$

Published on 15 Apr 2026 - 7:37

45

Views

Can a closed manifold defines a submersion over a manifold with non-empty boundary?

Published on 14 Apr 2026 - 13:44

442

Views

Proof verification: use transversality to prove that a smooth bundle admits a certain section

Published on 12 Apr 2026 - 0:02

837

Views

Existence of specific sections of vector bundles over a manifold

Published on 14 Apr 2026 - 20:54

84

Views

Prove that singular homology groups $H_k(M_{diff}, \mathbb{Z})$ and $H_k(M, \mathbb{Z})$ are isomorphic

Published on 10 Apr 2026 - 1:57

211

Views

How does the manifold topology affect the properties of the metric tensor?

Published on 12 Apr 2026 - 8:14

77

Views

Reference requested for homotopy theory theorem

Published on 25 Mar 2026 - 12:22

157

Views

Notation of coordinate functions on manifolds

Published on 11 Apr 2026 - 9:04

108

Views

Tranversal paths between two points

Published on 09 Apr 2026 - 14:41

123

Views

Why velocity and accelleration must be linearly independent?

Published on 13 Apr 2026 - 20:36

582

Views

Any two non-separating curves on a surface are equivalent

Published on 15 May 2026 - 23:57

92

Views

Asymmetry between definitions of curvature in 2-space and 3-space

Published on 12 Apr 2026 - 11:52

79

Views

Why should this manifold be an open set?

Published on 12 Apr 2026 - 20:32

List Question

What is the essence of ``the naturality of the cap product''?

Perelman's theorem in dimensions other than 3 (and 4) - why is it "easy"?

$\chi(A\cup B)=\chi(A)+\chi(B)-\chi(A\cap B)$

Can a closed manifold defines a submersion over a manifold with non-empty boundary?

Proof verification: use transversality to prove that a smooth bundle admits a certain section

Existence of specific sections of vector bundles over a manifold

Prove that singular homology groups $H_k(M_{diff}, \mathbb{Z})$ and $H_k(M, \mathbb{Z})$ are isomorphic

How does the manifold topology affect the properties of the metric tensor?

Reference requested for homotopy theory theorem

Notation of coordinate functions on manifolds

Tranversal paths between two points

Why velocity and accelleration must be linearly independent?

Any two non-separating curves on a surface are equivalent

Asymmetry between definitions of curvature in 2-space and 3-space

Why should this manifold be an open set?

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