Question

How do I prove that a connected Manifold of dimension m can't have another dimension?

score 47 · Answer 1 · 2026-03-28 13:41:59

47

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How do I prove that a connected Manifold of dimension m can't have another dimension?

Published on 28 Mar 2026 - 13:41

score 205 · Answer 2 · 2026-04-12 02:09:38

205

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Lifting maps of Sphere to the Torus

Published on 12 Apr 2026 - 2:09

score 41 · Answer 3 · 2024-01-13 09:11:31

41

Views

Finitely many intersections between a smooth curve and the boundary of a ball

Published on 13 Jan 2024 - 9:11

score 37 · Answer 4 · 2026-04-01 08:09:06

37

Views

Banach-Bundle: What is differentiability on "only" topological space?

Published on 01 Apr 2026 - 8:09

score 90 · Answer 5 · 2026-04-03 07:25:43

90

Views

Vector Field Degrees

Published on 03 Apr 2026 - 7:25

score 105 · Answer 6 · 2026-04-03 22:26:53

105

Views

On the induced map in cohomology

Published on 03 Apr 2026 - 22:26

score 166 · Answer 7 · 2024-01-14 20:25:31

166

Views

Smooth manifold's definition and initial topology

Published on 14 Jan 2024 - 20:25

score 68 · Answer 8 · 2026-04-09 10:04:00

68

Views

Definition of Lefschetz Number in Bott&Tu and in Gullemin&Pollack Differs by a sign?

Published on 09 Apr 2026 - 10:04

score 48 · Answer 9 · 2026-03-28 14:06:32

48

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Let $F: \mathbb R^m \to \mathbb R^n$ be smooth, $F(0) = 0$. Let $H(t,x) = \frac{F(tx)}{t}$ if $t \neq 0$ and $DF|_0(x)$ otherwise. Show $H$ is smooth

Published on 28 Mar 2026 - 14:06

score 61 · Answer 10 · 2026-03-25 09:50:11

61

Views

Let $f: \mathbb C \to \mathbb C$ be a proper smooth map with continuous extension $F : \mathbb C P^1 \to \mathbb C P^1$. Must $F$ be smooth?

Published on 25 Mar 2026 - 9:50

score 92 · Answer 11 · 2024-01-17 00:09:24

92

Views

Prove that if $F: \mathbb R^n \to \mathbb R^n$, wth $n \geq 2$, is a smooth proper map with finitely many critical points, then $F$ is surjective

Published on 17 Jan 2024 - 0:09

score 103 · Answer 12 · 2024-01-17 04:03:42

103

Views

What is $X\otimes Y$ where $X,Y$ are vector fields?

Published on 17 Jan 2024 - 4:03

score 64 · Answer 13 · 2026-03-25 16:09:12

64

Views

3-connection on nontrivial 3-manifold

Published on 25 Mar 2026 - 16:09

score 61 · Answer 14 · 2026-03-27 06:17:04

61

Views

Compactly supported de Rham cohomology groups of $M\times \mathbb{R}^{n}$

Published on 27 Mar 2026 - 6:17

score 65 · Answer 15 · 2026-04-12 19:33:02

65

Views

Pseudo-isotopy of a surface implies isotopy?

Published on 12 Apr 2026 - 19:33

List Question

How do I prove that a connected Manifold of dimension m can't have another dimension?

Lifting maps of Sphere to the Torus

Finitely many intersections between a smooth curve and the boundary of a ball

Banach-Bundle: What is differentiability on "only" topological space?

Vector Field Degrees

On the induced map in cohomology

Smooth manifold's definition and initial topology

Definition of Lefschetz Number in Bott&Tu and in Gullemin&Pollack Differs by a sign?

Let $F: \mathbb R^m \to \mathbb R^n$ be smooth, $F(0) = 0$. Let $H(t,x) = \frac{F(tx)}{t}$ if $t \neq 0$ and $DF|_0(x)$ otherwise. Show $H$ is smooth

Let $f: \mathbb C \to \mathbb C$ be a proper smooth map with continuous extension $F : \mathbb C P^1 \to \mathbb C P^1$. Must $F$ be smooth?

Prove that if $F: \mathbb R^n \to \mathbb R^n$, wth $n \geq 2$, is a smooth proper map with finitely many critical points, then $F$ is surjective

What is $X\otimes Y$ where $X,Y$ are vector fields?

3-connection on nontrivial 3-manifold

Compactly supported de Rham cohomology groups of $M\times \mathbb{R}^{n}$

Pseudo-isotopy of a surface implies isotopy?

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