Question

Covering a genus g surface with n disks, and conversely

score 452 · Answer 1 · 2026-04-10 12:15:53

452

Views

Covering a genus g surface with n disks, and conversely

Published on 10 Apr 2026 - 12:15

score 747 · Answer 2 · 2026-04-13 17:17:08

747

Views

There is no immersion of the Möbius band in the plane.

Published on 13 Apr 2026 - 17:17

score 814 · Answer 3 · 2026-04-14 03:47:43

814

Views

Proof the degree of a reflection through a hyperplane is −1.

Published on 14 Apr 2026 - 3:47

score 48 · Answer 4 · 2026-04-16 12:19:46

48

Views

$\vec{v}(x)/|\vec{v}(x)|$ extends to the annulus bounded by the two spheres.

Published on 16 Apr 2026 - 12:19

score 37 · Answer 5 · 2026-04-14 17:09:53

37

Views

Why the degree of the directional map is the number of times $\vec{v}$ rotates?

Published on 14 Apr 2026 - 17:09

score 210 · Answer 6 · 2026-04-13 16:38:55

210

Views

A differential topology problem.

Published on 13 Apr 2026 - 16:38

score 2k · Answer 7 · 2026-04-09 19:57:18

2k

Views

Two definitions of smooth manifolds

Published on 09 Apr 2026 - 19:57

score 100 · Answer 8 · 2026-04-13 20:46:22

100

Views

$1$-forms of coordinate function $dx_i(z)(a_1, \dots, a_k) = a_i$.

Published on 13 Apr 2026 - 20:46

score 311 · Answer 9 · 2026-04-12 14:38:34

311

Views

Show that $d\phi = \sum \frac{\partial \phi}{\partial x_i}dx_i.$

Published on 12 Apr 2026 - 14:38

score 442 · Answer 10 · 2026-04-14 12:06:56

442

Views

Fill in the hole for the proof for $f^(w \wedge \theta) = (f^w) \wedge (f^* \theta)$

Published on 14 Apr 2026 - 12:06

score 1.4k · Answer 11 · 2026-04-09 18:21:58

1.4k

Views

Definition of pullback.

Published on 09 Apr 2026 - 18:21

score 192 · Answer 12 · 2026-04-14 20:50:11

192

Views

How to show the smooth map $f : T^2 \to S^3$ is an orientation-preserving diffeomorphism?

Published on 14 Apr 2026 - 20:50

score 215 · Answer 13 · 2026-04-15 22:20:53

215

Views

$f: X \to Y$ is a smooth map and $\omega$ is a $p$-form on $Y$, what is $\omega[f(x)]$?

Published on 15 Apr 2026 - 22:20

score 378 · Answer 14 · 2026-04-11 17:43:01

378

Views

Pullback expanded form.

Published on 11 Apr 2026 - 17:43

score 2.2k · Answer 15 · 2026-04-16 11:46:44

2.2k

Views

$f^(w \wedge \theta) = (f^w) \wedge (f^* \theta)$

Published on 16 Apr 2026 - 11:46

List Question

Covering a genus g surface with n disks, and conversely

There is no immersion of the Möbius band in the plane.

Proof the degree of a reflection through a hyperplane is −1.

$\vec{v}(x)/|\vec{v}(x)|$ extends to the annulus bounded by the two spheres.

Why the degree of the directional map is the number of times $\vec{v}$ rotates?

A differential topology problem.

Two definitions of smooth manifolds

$1$-forms of coordinate function $dx_i(z)(a_1, \dots, a_k) = a_i$.

Show that $d\phi = \sum \frac{\partial \phi}{\partial x_i}dx_i.$

Fill in the hole for the proof for $f^(w \wedge \theta) = (f^w) \wedge (f^* \theta)$

Definition of pullback.

How to show the smooth map $f : T^2 \to S^3$ is an orientation-preserving diffeomorphism?

$f: X \to Y$ is a smooth map and $\omega$ is a $p$-form on $Y$, what is $\omega[f(x)]$?

Pullback expanded form.

$f^(w \wedge \theta) = (f^w) \wedge (f^* \theta)$

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