Question

How to see that existence non-trivial parallel $p$-form implies $b_p\geq 1$ using De Rham cohomology?

score 134 · Answer 1 · 2026-04-16 01:59:39

134

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How to see that existence non-trivial parallel $p$-form implies $b_p\geq 1$ using De Rham cohomology?

Published on 16 Apr 2026 - 1:59

score 409 · Answer 2 · 2026-04-12 23:44:41

409

Views

Using quotient to show that a map $\mathbb{RP}^2\rightarrow\mathbb{R}^3$ is an immersion at all but six points

Published on 12 Apr 2026 - 23:44

score 221 · Answer 3 · 2026-04-13 23:13:01

221

Views

Proof verification - Zero section of a bundle is homotopic to a section transverse to $M$?

Published on 13 Apr 2026 - 23:13

score 35 · Answer 4 · 2026-04-13 07:15:22

35

Views

What could differential operator be?

Published on 13 Apr 2026 - 7:15

score 104 · Answer 5 · 2026-04-10 16:15:50

104

Views

A reference book to study Thom-Pontryagin Theory from basic

Published on 10 Apr 2026 - 16:15

score 47 · Answer 6 · 2026-04-16 11:58:14

47

Views

Prove that a $(n-1)$-manifold $M$ disconnects the euclidean space into two connected part

Published on 16 Apr 2026 - 11:58

score 69 · Answer 7 · 2026-04-14 20:36:12

69

Views

Different Topologies for a Tangent Bundle $TM$ of a smooth manifold $M$

Published on 14 Apr 2026 - 20:36

score 24 · Answer 8 · 2026-04-14 17:50:20

24

Views

regular value of homotopy F is regular value for F_t

Published on 14 Apr 2026 - 17:50

score 349 · Answer 9 · 2026-04-13 03:58:02

349

Views

How to prove that $\phi=f:S\rightarrow \mathbb{S}^2$ is a bijection without using $h$?

Published on 13 Apr 2026 - 3:58

score 170 · Answer 10 · 2026-05-10 22:02:45

170

Views

Relationship between the Reeb field of a contact manifold and the Reeb field of a contact submanifold

Published on 10 May 2026 - 22:02

score 46 · Answer 11 · 2026-04-15 07:01:33

46

Views

What's the differential of a couple

Published on 15 Apr 2026 - 7:01

score 302 · Answer 12 · 2026-04-08 07:30:37

302

Views

Covariant derivatives along curves proof explanation

Published on 08 Apr 2026 - 7:30

score 357 · Answer 13 · 2026-04-13 11:47:27

357

Views

Intersection of two submanifolds with dimension condition

Published on 13 Apr 2026 - 11:47

score 129 · Answer 14 · 2026-04-14 05:15:04

129

Views

Existence of diffeomorphism of high-dimensional manifold with boundary $M$ and $M\#\Sigma$.

Published on 14 Apr 2026 - 5:15

score 56 · Answer 15 · 2026-04-10 20:53:37

56

Views

How to calculate a rank of a map?

Published on 10 Apr 2026 - 20:53

List Question

How to see that existence non-trivial parallel $p$-form implies $b_p\geq 1$ using De Rham cohomology?

Using quotient to show that a map $\mathbb{RP}^2\rightarrow\mathbb{R}^3$ is an immersion at all but six points

Proof verification - Zero section of a bundle is homotopic to a section transverse to $M$?

What could differential operator be?

A reference book to study Thom-Pontryagin Theory from basic

Prove that a $(n-1)$-manifold $M$ disconnects the euclidean space into two connected part

Different Topologies for a Tangent Bundle $TM$ of a smooth manifold $M$

regular value of homotopy F is regular value for F_t

How to prove that $\phi=f:S\rightarrow \mathbb{S}^2$ is a bijection without using $h$?

Relationship between the Reeb field of a contact manifold and the Reeb field of a contact submanifold

What's the differential of a couple

Covariant derivatives along curves proof explanation

Intersection of two submanifolds with dimension condition

Existence of diffeomorphism of high-dimensional manifold with boundary $M$ and $M\#\Sigma$.

How to calculate a rank of a map?

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