List questions from differential-topology

Published on 15 Nov 2014 - 15:06

2.7k

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Coordinate-free definition of integration of differential forms?

Published on 30 Mar 2026 - 8:01

493

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Suppose that $Z$ is a hyperspace in the oriented manifold $Y$, as sub manifold of codimension $1$. Prove that following statement are equivalent

Published on 15 Nov 2014 - 17:00

948

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Prove that the Möbius band is not orientable.

Published on 15 Nov 2014 - 17:13

716

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Why is the pole generally outside the contour loop when its outside the contour loop in 2D?

Published on 15 Nov 2014 - 21:30

187

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Prove that a map $f:S^1→S^1$ extends to the whole ball $B=\{|z|≤1\}$ if and only if $deg(f)=0$

Published on 16 Nov 2014 - 21:42

763

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How to orient a manifold in the Euclidean space?

Published on 18 Nov 2014 - 18:40

291

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Embedding counterexample

Published on 18 Nov 2014 - 21:37

2.8k

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Smooth homotopy

Published on 19 Nov 2014 - 0:19

68

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Smooth maps homotopic to the inclusion - updated.

Published on 19 Nov 2014 - 9:34

51

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Geometrical Explanation of Borsuk Theorem

Published on 19 Nov 2014 - 10:51

94

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1-forms as a direct sum

Published on 26 Mar 2026 - 3:10

417

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Only one fixed point for $f:\bar{\mathbb{D}}\rightarrow\bar{\mathbb{D}}$ on the boundary.

Published on 27 Mar 2026 - 19:32

179

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How to prove that a certain set is a submanifold.

Published on 19 Nov 2014 - 17:19

243

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Preimage of 0 for a differentiable function.

Published on 19 Nov 2014 - 19:01

List Question

Extension of a map $g:\overline{B_1^n}\to \mathbb{R}^2$

Coordinate-free definition of integration of differential forms?

Suppose that $Z$ is a hyperspace in the oriented manifold $Y$, as sub manifold of codimension $1$. Prove that following statement are equivalent

Prove that the Möbius band is not orientable.

Why is the pole generally outside the contour loop when its outside the contour loop in 2D?

Prove that a map $f:S^1→S^1$ extends to the whole ball $B=\{|z|≤1\}$ if and only if $deg(f)=0$

How to orient a manifold in the Euclidean space?

Embedding counterexample

Smooth homotopy

Smooth maps homotopic to the inclusion - updated.

Geometrical Explanation of Borsuk Theorem

1-forms as a direct sum

Only one fixed point for $f:\bar{\mathbb{D}}\rightarrow\bar{\mathbb{D}}$ on the boundary.

How to prove that a certain set is a submanifold.

Preimage of 0 for a differentiable function.

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