List questions from differential-topology

Published on 24 Mar 2024 - 12:29

79

Views

How to compute degree of $f: S^1\to S^1$ defined as $e^{ix}\mapsto e^{iax}$?

Published on 27 Mar 2026 - 6:17

22

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Class in $H^1(T^2)$ that is not dual to closed 1-dim submanifold of $T^2$

Published on 09 Apr 2026 - 12:03

45

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Example of smooth map that doesn't has constant rank

Published on 25 Mar 2024 - 5:50

77

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In complex geometry, is an holomorphic function continuous by definition?

Published on 10 Apr 2026 - 9:54

38

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Calculating distance on riemannian manifold

Published on 26 Mar 2024 - 6:08

96

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Prove that if a smooth manifold $M$ is contractible then every vector bundle over $M$ is trivial

Published on 01 Apr 2026 - 14:30

80

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Derivative of the map $f:S^1\to S^1: z\mapsto z^n$ is orientation preserving or not?

Published on 27 Mar 2024 - 20:06

45

Views

Algebraic cancelling handles

Published on 28 Mar 2024 - 16:06

79

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How to pull back the differential form $\omega = \frac{-ydx+xdy}{\sqrt{x^2+y^2}}$ to $S^2$

Published on 30 Mar 2024 - 21:46

66

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making sense of calculations in the proof that the image of an embedding is an embedded submanifold

Published on 26 Mar 2026 - 21:27

632

Views

What is the definition of a properly-immersed arc?

Published on 12 Apr 2026 - 11:48

1.1k

Views

Find the Poincare Dual of a ray in $\mathbb{R}^2-\{0\}$

Published on 13 Apr 2026 - 20:08

511

Views

Is it possible for a manifold to have a normal vector that is zero everywhere, if so, would this indicate that the manifold is non-orientable?

Published on 05 Jan 2015 - 7:28

1.3k

Views

What is a regular homotopy?

Published on 10 Apr 2026 - 15:47

List Question

Relation between sets of class $C^1$ and uniformly Lipschitz open sets.

How to compute degree of $f: S^1\to S^1$ defined as $e^{ix}\mapsto e^{iax}$?

Class in $H^1(T^2)$ that is not dual to closed 1-dim submanifold of $T^2$

Example of smooth map that doesn't has constant rank

In complex geometry, is an holomorphic function continuous by definition?

Calculating distance on riemannian manifold

Prove that if a smooth manifold $M$ is contractible then every vector bundle over $M$ is trivial

Derivative of the map $f:S^1\to S^1: z\mapsto z^n$ is orientation preserving or not?

Algebraic cancelling handles

How to pull back the differential form $\omega = \frac{-ydx+xdy}{\sqrt{x^2+y^2}}$ to $S^2$

making sense of calculations in the proof that the image of an embedding is an embedded submanifold

What is the definition of a properly-immersed arc?

Find the Poincare Dual of a ray in $\mathbb{R}^2-\{0\}$

Is it possible for a manifold to have a normal vector that is zero everywhere, if so, would this indicate that the manifold is non-orientable?

What is a regular homotopy?

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