List questions from differential-topology

292

Views

Any self-diffeomorphism of a compact manifold with boundary rel boundary can be isotoped to fix a collar of boundary

Published on 15 Apr 2026 - 14:40

248

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Normal bundles of $S^1$ in a Klein bottle

Published on 17 Apr 2026 - 2:35

43

Views

$I_2(X,Z) = 0$ for $X,Z$ manifolds in $\mathbb S^k$ of complementary dimension

Published on 11 May 2026 - 5:25

61

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Betti number of sphere and vector-Laplacian

Published on 16 Apr 2026 - 9:59

355

Views

Local coordinates of one form on a principal bundle

Published on 16 May 2026 - 15:27

82

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calculate the kernel of a germ map

Published on 10 Apr 2026 - 22:05

66

Views

A counterexample for a Theorem of Hirsch on the Cohomology of a nilpotent group over a finite dimensional vector space

Published on 15 Apr 2026 - 2:03

53

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Why the Euler characteristics of a compact connected lagrangian submanifold of $\mathbb{R}^4$ is zero?

Published on 10 Apr 2026 - 6:58

429

Views

there exists no non vanishing vector field on $S^2$

Published on 16 Apr 2026 - 13:12

812

Views

The hairy ball theorem, from Brouwer's fixed point.

Published on 14 Apr 2026 - 13:01

142

Views

How to understand and use the Whitney stratification theorem?

Published on 10 Apr 2026 - 15:31

179

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Any 3 manifold can be realized as a boundary of a 4 manifold?

Published on 16 Apr 2026 - 5:30

65

Views

A smooth fiber bundle $S^1\times S^3\to \Sigma$ where $\Sigma$ is a closed surface

Published on 12 Apr 2026 - 23:24

93

Views

The total space of an $S^2$ bundle over a closed surface is a ruled surface

Published on 14 Apr 2026 - 12:05

140

Views

Why do positive densities exist on any smooth manifold?

Published on 17 Apr 2026 - 21:57

List Question

Any self-diffeomorphism of a compact manifold with boundary rel boundary can be isotoped to fix a collar of boundary

Normal bundles of $S^1$ in a Klein bottle

$I_2(X,Z) = 0$ for $X,Z$ manifolds in $\mathbb S^k$ of complementary dimension

Betti number of sphere and vector-Laplacian

Local coordinates of one form on a principal bundle

calculate the kernel of a germ map

A counterexample for a Theorem of Hirsch on the Cohomology of a nilpotent group over a finite dimensional vector space

Why the Euler characteristics of a compact connected lagrangian submanifold of $\mathbb{R}^4$ is zero?

there exists no non vanishing vector field on $S^2$

The hairy ball theorem, from Brouwer's fixed point.

How to understand and use the Whitney stratification theorem?

Any 3 manifold can be realized as a boundary of a 4 manifold?

A smooth fiber bundle $S^1\times S^3\to \Sigma$ where $\Sigma$ is a closed surface

The total space of an $S^2$ bundle over a closed surface is a ruled surface

Why do positive densities exist on any smooth manifold?

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