List questions from manifolds

Published on 10 Apr 2026 - 8:15

1.2k

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how to prove that every low-dimensional topological manifold has a unique smooth structure up to diffeomorphism?

Published on 26 Apr 2026 - 2:21

287

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Wedge product of closed form each with integral periods has integral period?

Published on 26 Apr 2026 - 3:52

225

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What is the manifold underlying the Lie group $SU(p,q)$?

Published on 04 May 2026 - 14:54

149

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Two smoothly homotopic smooth maps induce same maps on de Rham cohomology

Published on 26 Apr 2026 - 3:50

822

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Does there exist a $1$-form $\alpha$ with $d\alpha = \omega$?

Published on 08 Apr 2026 - 16:22

70

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Smooth representative $f: S^{2n - 1} \to S^n$, do we have $f^*\omega = d\alpha$?

Published on 15 Apr 2026 - 21:47

77

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Is $H([f]) = \int_{S^{2n - 1}} \alpha \wedge d\alpha$ independent of all choices, defines a map $H: \pi_{2n - 1}(S^n) \to \mathbb{Z}$?

Published on 26 Apr 2026 - 3:54

157

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Map of constant rank

Published on 17 Apr 2026 - 1:08

457

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Topological manifold but not "smooth"

Published on 12 Apr 2026 - 19:43

203

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One-sided submanifolds in Hempel's 3-Manifolds

Published on 26 Mar 2026 - 23:11

85

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Prove that if $f$ is a solution of the heat equation.

Published on 12 Apr 2026 - 6:49

27

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Given a one-t0-one function f that maps M onto an arbitrary set A, prove there is a unique way to make A a manifold s.t. f becomes a diffeomorphism.

Published on 15 Apr 2026 - 20:38

169

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Show that $M$ is a 2-dimensional submanifold.

Published on 14 Apr 2026 - 9:54

91

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Why is the dimension of a real submanifold uniqely determined?

Published on 16 Apr 2026 - 0:59

List Question

Visualizing the evolution of a Riemannian metric

how to prove that every low-dimensional topological manifold has a unique smooth structure up to diffeomorphism?

Wedge product of closed form each with integral periods has integral period?

What is the manifold underlying the Lie group $SU(p,q)$?

Two smoothly homotopic smooth maps induce same maps on de Rham cohomology

Does there exist a $1$-form $\alpha$ with $d\alpha = \omega$?

Smooth representative $f: S^{2n - 1} \to S^n$, do we have $f^*\omega = d\alpha$?

Is $H([f]) = \int_{S^{2n - 1}} \alpha \wedge d\alpha$ independent of all choices, defines a map $H: \pi_{2n - 1}(S^n) \to \mathbb{Z}$?

Map of constant rank

Topological manifold but not "smooth"

One-sided submanifolds in Hempel's 3-Manifolds

Prove that if $f$ is a solution of the heat equation.

Given a one-t0-one function f that maps M onto an arbitrary set A, prove there is a unique way to make A a manifold s.t. f becomes a diffeomorphism.

Show that $M$ is a 2-dimensional submanifold.

Why is the dimension of a real submanifold uniqely determined?

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