Question

What is the intrinsic ( without any reference to embedding ) and coordinate free , basis free definition of a 2 sphere as a differentiable manifold?

score 202 · Answer 1 · 2019-02-10 17:06:29

What is the intrinsic ( without any reference to embedding ) and coordinate free , basis free definition of a 2 sphere as a differentiable manifold?

score 396 · Answer 2 · 2026-03-26 05:55:56

396

Views

On the proof of the Whitney trick (from Scorpan's book)

Published on 26 Mar 2026 - 5:55

score 81 · Answer 3 · 2026-03-26 23:11:11

81

Views

Lower bound of embedding dimension for finite CW-Complex of dimension $d$

Published on 26 Mar 2026 - 23:11

score 124 · Answer 4 · 2026-03-26 23:11:17

124

Views

How do I show $X_{\omega(Y,Z)}=-[Y,Z]$?

Published on 26 Mar 2026 - 23:11

score 468 · Answer 5 · 2026-03-26 23:09:52

468

Views

Classification of contractible 4-manifolds

Published on 26 Mar 2026 - 23:09

score 701 · Answer 6 · 2019-02-12 11:08:17

701

Views

What is the natural isomorphism between the tangent space of a product manifold and the product of the tangent spaces?

Published on 12 Feb 2019 - 11:08

score 173 · Answer 7 · 2026-03-25 06:12:20

173

Views

Why does any connected closed $m$-manifold that can be embedded in $E^{m+1}$ bounds a compact connected $(m+1)$-manifold?

Published on 25 Mar 2026 - 6:12

score 160 · Answer 8 · 2019-02-13 17:31:40

160

Views

Spaces of submanifolds

Published on 13 Feb 2019 - 17:31

score 74 · Answer 9 · 2019-02-14 14:28:06

74

Views

A differentiable manifold class $C^k$ but not class $C^{k+1}$

Published on 14 Feb 2019 - 14:28

score 294 · Answer 10 · 2019-02-14 15:37:24

294

Views

Visualizing tangent space from its definition

Published on 14 Feb 2019 - 15:37

score 103 · Answer 11 · 2019-02-14 17:10:31

103

Views

Functions from an $n$-dimensional hypercube to $\mathbb{R}^m$ when $n >m$.

Published on 14 Feb 2019 - 17:10

score 540 · Answer 12 · 2026-03-27 01:13:21

540

Views

Euler’s Characteristic for nonorientable surfaces?

Published on 27 Mar 2026 - 1:13

score 774 · Answer 13 · 2026-03-25 19:04:22

774

Views

Find wrapping angle of helix on a torus

Published on 25 Mar 2026 - 19:04

score 288 · Answer 14 · 2019-02-16 03:39:49

288

Views

Surjective functions from a $n$-dimensional hypercube to $\mathbb{R}^m$ when $n > m$

Published on 16 Feb 2019 - 3:39

score 58 · Answer 15 · 2026-03-23 04:30:22

58

Views

Connecting the Fibres of a Lefschetz Fibration With Disconnected Fibres.

Published on 23 Mar 2026 - 4:30

List Question

What is the intrinsic ( without any reference to embedding ) and coordinate free , basis free definition of a 2 sphere as a differentiable manifold?

On the proof of the Whitney trick (from Scorpan's book)

Lower bound of embedding dimension for finite CW-Complex of dimension $d$

How do I show $X_{\omega(Y,Z)}=-[Y,Z]$?

Classification of contractible 4-manifolds

What is the natural isomorphism between the tangent space of a product manifold and the product of the tangent spaces?

Why does any connected closed $m$-manifold that can be embedded in $E^{m+1}$ bounds a compact connected $(m+1)$-manifold?

Spaces of submanifolds

A differentiable manifold class $C^k$ but not class $C^{k+1}$

Visualizing tangent space from its definition

Functions from an $n$-dimensional hypercube to $\mathbb{R}^m$ when $n >m$.

Euler’s Characteristic for nonorientable surfaces?

Find wrapping angle of helix on a torus

Surjective functions from a $n$-dimensional hypercube to $\mathbb{R}^m$ when $n > m$

Connecting the Fibres of a Lefschetz Fibration With Disconnected Fibres.

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