Question

Isn't there a better way to put the canonical smooth structure on the $n$-sphere?

score 1.1k · Answer 1 · 2026-04-12 07:10:40

1.1k

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Isn't there a better way to put the canonical smooth structure on the $n$-sphere?

Published on 12 Apr 2026 - 7:10

score 60 · Answer 2 · 2026-04-16 00:27:57

60

Views

If $M\subset \mathbb{R}^d$ is a manifold of dimension $m$ and $U\subset \mathbb{R}^d$ is open, then $M\cap U$ is not a open.

Published on 16 Apr 2026 - 0:27

score 488 · Answer 3 · 2026-04-11 05:39:12

488

Views

Tangent space to noncompact Stiefel manifold

Published on 11 Apr 2026 - 5:39

score 285 · Answer 4 · 2026-04-12 23:22:49

285

Views

a question on topological manifolds and what topology provides

Published on 12 Apr 2026 - 23:22

score 1.6k · Answer 5 · 2026-04-16 12:08:40

1.6k

Views

Images of a familiar object in $\mathbb{R}^3$ mapped to $\mathbb{R}^2$ by Cantor/Peano/Hilbert

Published on 16 Apr 2026 - 12:08

score 168 · Answer 6 · 2026-04-16 06:35:48

168

Views

Why should the gradient of an $n-1$-manifold in $\mathbb R^n$ be nonzero?

Published on 16 Apr 2026 - 6:35

score 1.3k · Answer 7 · 2026-04-24 07:20:15

1.3k

Views

parallel vector field

Published on 24 Apr 2026 - 7:20

score 470 · Answer 8 · 2026-04-24 07:22:15

470

Views

Normal coordinate parallel along radial geodesics?

Published on 24 Apr 2026 - 7:22

score 1k · Answer 9 · 2026-04-17 07:19:49

1k

Views

If $\phi: M_1 \to M_2$ a diffeomorphism between diff. manifolds, prove that if $M_2$ is orientable then so is $M_1$

Published on 17 Apr 2026 - 7:19

score 809 · Answer 10 · 2026-04-15 04:31:56

809

Views

Closed orientable 4-manifold with $H^1(M;\Bbb Z_2)=\Bbb Z_2$ and non-zero cup product $H^1\times H^1\to H^2$

Published on 15 Apr 2026 - 4:31

score 559 · Answer 11 · 2026-04-14 03:10:59

559

Views

Lie Derivative of Connection 1 form

Published on 14 Apr 2026 - 3:10

score 70 · Answer 12 · 2026-04-13 11:47:18

70

Views

Existence of a open set between a compact and an open set

Published on 13 Apr 2026 - 11:47

score 2.5k · Answer 13 · 2026-04-12 13:16:47

2.5k

Views

Prove that the antipodal mapping is an isometry on $S^n$. Help understanding the proof.

Published on 12 Apr 2026 - 13:16

score 410 · Answer 14 · 2026-04-14 18:14:54

410

Views

The set of all matrix with rank $n-1$ is a hypersurface.

Published on 14 Apr 2026 - 18:14

score 392 · Answer 15 · 2026-04-11 00:58:22

392

Views

What are the 8 non-compact Euclidean 3-manifolds?

Published on 11 Apr 2026 - 0:58

List Question

Isn't there a better way to put the canonical smooth structure on the $n$-sphere?

If $M\subset \mathbb{R}^d$ is a manifold of dimension $m$ and $U\subset \mathbb{R}^d$ is open, then $M\cap U$ is not a open.

Tangent space to noncompact Stiefel manifold

a question on topological manifolds and what topology provides

Images of a familiar object in $\mathbb{R}^3$ mapped to $\mathbb{R}^2$ by Cantor/Peano/Hilbert

Why should the gradient of an $n-1$-manifold in $\mathbb R^n$ be nonzero?

parallel vector field

Normal coordinate parallel along radial geodesics?

If $\phi: M_1 \to M_2$ a diffeomorphism between diff. manifolds, prove that if $M_2$ is orientable then so is $M_1$

Closed orientable 4-manifold with $H^1(M;\Bbb Z_2)=\Bbb Z_2$ and non-zero cup product $H^1\times H^1\to H^2$

Lie Derivative of Connection 1 form

Existence of a open set between a compact and an open set

Prove that the antipodal mapping is an isometry on $S^n$. Help understanding the proof.

The set of all matrix with rank $n-1$ is a hypersurface.

What are the 8 non-compact Euclidean 3-manifolds?

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