Question

Does open map imply dimension of domain is greater than or equal to dimension of range? (please don't use sard's theorem)

score 311 · Answer 1 · 2026-04-16 11:32:05

311

Views

Does open map imply dimension of domain is greater than or equal to dimension of range? (please don't use sard's theorem)

Published on 16 Apr 2026 - 11:32

score 325 · Answer 2 · 2026-04-10 12:21:40

325

Views

Is open (topological) smooth embedding equivalent to injective local (homeomorphism) diffeomorphism?

Published on 10 Apr 2026 - 12:21

score 314 · Answer 3 · 2026-04-12 08:21:26

314

Views

Oriented Atlas for $\mathbb{RP}^3$

Published on 12 Apr 2026 - 8:21

score 178 · Answer 4 · 2026-04-12 00:19:55

178

Views

Coordinates in Local Immersion Theorem

Published on 12 Apr 2026 - 0:19

score 132 · Answer 5 · 2026-04-14 00:39:36

132

Views

Classification of free $S^1$-actions on $S^2\times S^1$

Published on 14 Apr 2026 - 0:39

score 69 · Answer 6 · 2026-04-14 14:07:11

69

Views

Show that the intersection of $U(n)$ with symmetric matrices is a submanifold of $U(n)$.

Published on 14 Apr 2026 - 14:07

score 112 · Answer 7 · 2026-04-13 17:18:55

112

Views

Prove $H^{k}_\text{deRham} (M \times S^{n}) \cong H^{k}_\text{deRham} (M) \bigoplus H^{k-n}_\text{deRham} (M)$ using Mayer-Vietoris

Published on 13 Apr 2026 - 17:18

score 256 · Answer 8 · 2026-04-17 12:50:40

256

Views

Exactness of closed 1-forms on toruses

Published on 17 Apr 2026 - 12:50

score 448 · Answer 9 · 2026-04-13 08:12:41

448

Views

Is every compact $n$-manifold that immerses in $\mathbb{R}^{n+1}$ smoothable?

Published on 13 Apr 2026 - 8:12

score 143 · Answer 10 · 2026-04-11 14:24:29

143

Views

Details about the Brouwer fixed-point theorem

Published on 11 Apr 2026 - 14:24

score 105 · Answer 11 · 2026-05-11 06:15:38

105

Views

Orientation-reversing involution on $S^3$, commuting with a circle action?

Published on 11 May 2026 - 6:15

score 70 · Answer 12 · 2026-04-16 12:43:31

70

Views

How can two $C^1$ transition map form a $C^{\infty}$ compatible charts?

Published on 16 Apr 2026 - 12:43

score 194 · Answer 13 · 2026-04-13 14:38:10

194

Views

Are these equivalent for regular submanifold? Open, image of local diffeomorphism, image of injective local diffeomorphism

Published on 13 Apr 2026 - 14:38

score 43 · Answer 14 · 2026-05-11 04:10:29

43

Views

If $\alpha$ is an arbitrary simple curve that cuts transversaly a compact surface the set of common points it can be infinity?

Published on 11 May 2026 - 4:10

score 423 · Answer 15 · 2026-04-13 19:50:22

423

Views

Do we always get the same dimension regardless of the manifold/topological structure?

Published on 13 Apr 2026 - 19:50

List Question

Does open map imply dimension of domain is greater than or equal to dimension of range? (please don't use sard's theorem)

Is open (topological) smooth embedding equivalent to injective local (homeomorphism) diffeomorphism?

Oriented Atlas for $\mathbb{RP}^3$

Coordinates in Local Immersion Theorem

Classification of free $S^1$-actions on $S^2\times S^1$

Show that the intersection of $U(n)$ with symmetric matrices is a submanifold of $U(n)$.

Prove $H^{k}_\text{deRham} (M \times S^{n}) \cong H^{k}_\text{deRham} (M) \bigoplus H^{k-n}_\text{deRham} (M)$ using Mayer-Vietoris

Exactness of closed 1-forms on toruses

Is every compact $n$-manifold that immerses in $\mathbb{R}^{n+1}$ smoothable?

Details about the Brouwer fixed-point theorem

Orientation-reversing involution on $S^3$, commuting with a circle action?

How can two $C^1$ transition map form a $C^{\infty}$ compatible charts?

Are these equivalent for regular submanifold? Open, image of local diffeomorphism, image of injective local diffeomorphism

If $\alpha$ is an arbitrary simple curve that cuts transversaly a compact surface the set of common points it can be infinity?

Do we always get the same dimension regardless of the manifold/topological structure?

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