Question

Suppose $M$ has trivial 1-st de Rham cohomology group. For which integers $k$ does there exist a smooth map $f : M → T^n$ of degree $k$?

score 95 · Answer 1 · 2026-03-25 14:25:14

95

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Suppose $M$ has trivial 1-st de Rham cohomology group. For which integers $k$ does there exist a smooth map $f : M → T^n$ of degree $k$?

Published on 25 Mar 2026 - 14:25

score 211 · Answer 2 · 2016-07-13 11:52:09

211

Views

Smooth homotopy between $\Bbb R^2-\{0\}$ and $S^1$

Published on 13 Jul 2016 - 11:52

score 2k · Answer 3 · 2016-07-15 01:20:40

2k

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Origins of Differential Geometry and the Notion of Manifold

Published on 15 Jul 2016 - 1:20

score 669 · Answer 4 · 2026-04-06 12:40:35

669

Views

Preimage of tubular neighborhood

Published on 06 Apr 2026 - 12:40

score 134 · Answer 5 · 2026-03-26 11:04:15

134

Views

Why a Riemannian manifold minus one point is not complete?

Published on 26 Mar 2026 - 11:04

score 964 · Answer 6 · 2026-03-28 06:01:03

964

Views

A Riemannian manifold with constant sectional curvature is Einstein.

Published on 28 Mar 2026 - 6:01

score 387 · Answer 7 · 2016-07-17 03:59:10

387

Views

Equivalences of the definition of smooth vector fields

Published on 17 Jul 2016 - 3:59

score 62 · Answer 8 · 2016-07-17 19:51:07

Where does $f(r,\varphi,\theta)=(r\sin{\theta}\cos{\varphi},r\sin{\theta}\sin{\varphi},r\cos{\theta})$ have a locally differentiable inversion?

score 2.4k · Answer 9 · 2026-03-26 22:16:24

2.4k

Views

When is the universal cover of a Riemannian manifold complete?

Published on 26 Mar 2026 - 22:16

score 1.1k · Answer 10 · 2026-03-27 23:48:53

1.1k

Views

Group of deck transformations acts properly discontinuously

Published on 27 Mar 2026 - 23:48

score 231 · Answer 11 · 2026-04-06 21:15:49

231

Views

Irreducible representations of the fundamental group of a closed surface in $SU(2)$

Published on 06 Apr 2026 - 21:15

score 100 · Answer 12 · 2026-03-30 03:21:33

100

Views

How do we call a map $F$ such that $F(g\cdot p)=\varphi(g)\cdot F(p)$?

Published on 30 Mar 2026 - 3:21

score 51 · Answer 13 · 2026-04-06 12:39:57

51

Views

Describe all smooth surfaces in $\mathbb{R}^3$ with coordinates $(x,y,z)$ such that the pullback of the one-form $\theta:=dy-zdx$ is identically zero.

Published on 06 Apr 2026 - 12:39

score 586 · Answer 14 · 2016-07-20 17:58:57

586

Views

Vector fields (on a manifold) and terminology

Published on 20 Jul 2016 - 17:58

score 183 · Answer 15 · 2026-04-06 19:04:48

183

Views

Construct a global smooth vector field

Published on 06 Apr 2026 - 19:04

List Question

Suppose $M$ has trivial 1-st de Rham cohomology group. For which integers $k$ does there exist a smooth map $f : M → T^n$ of degree $k$?

Smooth homotopy between $\Bbb R^2-\{0\}$ and $S^1$

Origins of Differential Geometry and the Notion of Manifold

Preimage of tubular neighborhood

Why a Riemannian manifold minus one point is not complete?

A Riemannian manifold with constant sectional curvature is Einstein.

Equivalences of the definition of smooth vector fields

Where does $f(r,\varphi,\theta)=(r\sin{\theta}\cos{\varphi},r\sin{\theta}\sin{\varphi},r\cos{\theta})$ have a locally differentiable inversion?

When is the universal cover of a Riemannian manifold complete?

Group of deck transformations acts properly discontinuously

Irreducible representations of the fundamental group of a closed surface in $SU(2)$

How do we call a map $F$ such that $F(g\cdot p)=\varphi(g)\cdot F(p)$?

Describe all smooth surfaces in $\mathbb{R}^3$ with coordinates $(x,y,z)$ such that the pullback of the one-form $\theta:=dy-zdx$ is identically zero.

Vector fields (on a manifold) and terminology

Construct a global smooth vector field

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