List questions from differential-topology

Published on 15 Apr 2026 - 2:56

67

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Who was the first person to prove the invariance of the Euler characteristic under triangulations?

Published on 13 Apr 2026 - 4:32

68

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Showing $\pi_{n+1} (S^n) = \mathbb{Z}_2$ for $n \geq 3$

Published on 12 Apr 2026 - 22:59

84

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Smoothing a collar twist.

Published on 11 Apr 2026 - 14:51

367

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Can a lagrangian submanifold of a 4-dimensional real space be diffeomorphic to sphere or real projective plane?

Published on 14 Apr 2026 - 13:44

97

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If $f:S\rightarrow \mathbb{R}^m$ is a map such that each $f|_{S_i}:S_i\rightarrow \mathbb{R}^m$ is differentiable, prove that $f$ is differentiable.

Published on 16 Apr 2026 - 18:25

32

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Is there a branched cover of $T^n \to S^n$?

Published on 14 Apr 2026 - 12:17

75

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If $M$ is connected and $\int_M \omega = 0,$ then $\omega = 0$?

Published on 13 Apr 2026 - 17:27

124

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If $\int_M \omega =0$ for all compact orientable manifold, then $\omega$ is closed

Published on 13 Apr 2026 - 17:27

154

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Why is this a smooth manifold?

Published on 15 Apr 2026 - 18:25

198

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Transversal intersection of graph and diagonal

Published on 17 Apr 2026 - 1:43

143

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Laplace's equation on the plane: how much boundary data must be specified to guarantee existence and uniqueness?

Published on 12 Apr 2026 - 8:58

353

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Show there exists no diffeomorphism between positive real line and a spiral

Published on 13 Apr 2026 - 23:49

102

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Existence of subspace disjoint from manifold

Published on 11 Apr 2026 - 11:59

138

Views

Writing down homeomorphisms in a formula

Published on 10 Apr 2026 - 14:19

List Question

Lift of a shortest loop is length minimizing

Who was the first person to prove the invariance of the Euler characteristic under triangulations?

Showing $\pi_{n+1} (S^n) = \mathbb{Z}_2$ for $n \geq 3$

Smoothing a collar twist.

Can a lagrangian submanifold of a 4-dimensional real space be diffeomorphic to sphere or real projective plane?

If $f:S\rightarrow \mathbb{R}^m$ is a map such that each $f|_{S_i}:S_i\rightarrow \mathbb{R}^m$ is differentiable, prove that $f$ is differentiable.

Is there a branched cover of $T^n \to S^n$?

If $M$ is connected and $\int_M \omega = 0,$ then $\omega = 0$?

If $\int_M \omega =0$ for all compact orientable manifold, then $\omega$ is closed

Why is this a smooth manifold?

Transversal intersection of graph and diagonal

Laplace's equation on the plane: how much boundary data must be specified to guarantee existence and uniqueness?

Show there exists no diffeomorphism between positive real line and a spiral

Existence of subspace disjoint from manifold

Writing down homeomorphisms in a formula

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