Question

Request for companion of Mariano Suárez-Alvarez's proof.

score 674 · Answer 1 · 2026-04-15 12:01:55

674

Views

Request for companion of Mariano Suárez-Alvarez's proof.

Published on 15 Apr 2026 - 12:01

score 131 · Answer 2 · 2026-04-11 21:38:45

131

Views

Assume that $f: X \rightarrow Y$ is a smooth map between two smooth manifolds.

Published on 11 Apr 2026 - 21:38

score 166 · Answer 3 · 2026-04-12 17:35:45

166

Views

The monodromy and cut planes.

Published on 12 Apr 2026 - 17:35

score 103 · Answer 4 · 2026-04-13 10:16:36

103

Views

Does $\mathrm{SL}(2, \mathbb{R})$ have a non-empty boundary?

Published on 13 Apr 2026 - 10:16

score 93 · Answer 5 · 2026-04-14 04:05:01

93

Views

$\forall M \in \mathrm{SL}(2, \mathbb{R})$ has a neighborhood diffeomorphic to $\mathbb{R}^3$?

Published on 14 Apr 2026 - 4:05

score 97 · Answer 6 · 2026-04-16 16:20:15

97

Views

$f$ extends to a smooth map $\tilde{f} : S^2 \to S^2$. - Is the proof legit?

Published on 16 Apr 2026 - 16:20

score 220 · Answer 7 · 2026-04-14 09:44:38

220

Views

Compute $d\omega$ and $\int_{S^2}\omega$.

Published on 14 Apr 2026 - 9:44

score 50 · Answer 8 · 2026-04-15 10:19:12

50

Views

For which values of $n$ does there exist a compact, oriented 3-manifold $X$.

Published on 15 Apr 2026 - 10:19

score 70 · Answer 9 · 2026-04-14 14:29:09

70

Views

The global Lefschetz number of $f$ vanishes. - Is this conterexample work?

Published on 14 Apr 2026 - 14:29

score 115 · Answer 10 · 2026-04-16 02:40:40

115

Views

$\int_{S^1} \beta = 0 \Rightarrow \beta$ is the differential of a function. - Is this proof legit?

Published on 16 Apr 2026 - 2:40

score 932 · Answer 11 · 2026-04-14 04:29:31

932

Views

Tangent bundles of exotic manifolds

Published on 14 Apr 2026 - 4:29

score 2.4k · Answer 12 · 2026-04-15 05:39:05

2.4k

Views

Diffeomorphisms are either both orientation-preserving or both orientation reversing.

Published on 15 Apr 2026 - 5:39

score 104 · Answer 13 · 2026-04-16 08:40:54

104

Views

Prove that $\mathcal{M}=\{(x, y) \in X \times Y : f(x) = g(y)\}$ is a smooth submanifold.

Published on 16 Apr 2026 - 8:40

score 5.1k · Answer 14 · 2026-04-13 20:53:26

5.1k

Views

A submersion $F : \mathcal{X} \to \mathcal{Y}$ must be surjective.

Published on 13 Apr 2026 - 20:53

score 2.9k · Answer 15 · 2026-04-11 08:20:40

2.9k

Views

When characteristic classes determine a bundle?

Published on 11 Apr 2026 - 8:20

List Question

Request for companion of Mariano Suárez-Alvarez's proof.

Assume that $f: X \rightarrow Y$ is a smooth map between two smooth manifolds.

The monodromy and cut planes.

Does $\mathrm{SL}(2, \mathbb{R})$ have a non-empty boundary?

$\forall M \in \mathrm{SL}(2, \mathbb{R})$ has a neighborhood diffeomorphic to $\mathbb{R}^3$?

$f$ extends to a smooth map $\tilde{f} : S^2 \to S^2$. - Is the proof legit?

Compute $d\omega$ and $\int_{S^2}\omega$.

For which values of $n$ does there exist a compact, oriented 3-manifold $X$.

The global Lefschetz number of $f$ vanishes. - Is this conterexample work?

$\int_{S^1} \beta = 0 \Rightarrow \beta$ is the differential of a function. - Is this proof legit?

Tangent bundles of exotic manifolds

Diffeomorphisms are either both orientation-preserving or both orientation reversing.

Prove that $\mathcal{M}=\{(x, y) \in X \times Y : f(x) = g(y)\}$ is a smooth submanifold.

A submersion $F : \mathcal{X} \to \mathcal{Y}$ must be surjective.

When characteristic classes determine a bundle?

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