List questions from differential-topology

Published on 10 May 2026 - 13:45

808

Views

Confusion about the definition of a parameterization of a smooth manifold

Published on 10 May 2026 - 12:34

643

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Cobordism and Boundary Theorem (Guillemin-Pollack)

Published on 29 Apr 2026 - 12:53

823

Views

Show that a complex polynomial has a root inside a disk

Published on 16 Apr 2026 - 17:24

192

Views

Find the image of a vector field

Published on 16 Apr 2026 - 14:32

204

Views

Coordinate independent way?

Published on 10 Apr 2026 - 12:15

111

Views

Unclear argument in Fulton's book on algebraic topology

Published on 10 May 2026 - 14:49

207

Views

Example of a manifold $M$ for which $TM$ and $T^*M$ are not isomorphic.

Published on 10 May 2026 - 17:15

418

Views

Codimension-1 submanifold as a inverse image of regular value.

Published on 29 Apr 2026 - 12:52

610

Views

Is the Transversality Homotopy Theorem wrong as it is stated in Lee‘s Introduction to smooth manifolds?

Published on 08 Apr 2026 - 6:02

961

Views

Show that $S^2$ is not diffeomorphic to the Torus.

Published on 29 Apr 2026 - 12:53

191

Views

Parallel transport on the $\mathbb{R}P^1$ tautological line bundle.

Published on 10 May 2026 - 17:13

228

Views

$f: \Bbb R \to \Bbb R^2$ given by $f(t) = (t^2,t^3)$ is an immersion at $0$.

Published on 14 Apr 2026 - 15:18

1.7k

Views

What is the Derivative of a Vector Field in a Manifold?

Published on 10 May 2026 - 14:49

159

Views

Are diffeomorphisms dense in $C^0(M)$ for a compact manifold M?

Published on 14 Apr 2026 - 3:47

List Question

Reference for Theorem About Closed and Exact Differential Forms

Confusion about the definition of a parameterization of a smooth manifold

Cobordism and Boundary Theorem (Guillemin-Pollack)

Show that a complex polynomial has a root inside a disk

Find the image of a vector field

Coordinate independent way?

Unclear argument in Fulton's book on algebraic topology

Example of a manifold $M$ for which $TM$ and $T^*M$ are not isomorphic.

Codimension-1 submanifold as a inverse image of regular value.

Is the Transversality Homotopy Theorem wrong as it is stated in Lee‘s Introduction to smooth manifolds?

Show that $S^2$ is not diffeomorphic to the Torus.

Parallel transport on the $\mathbb{R}P^1$ tautological line bundle.

$f: \Bbb R \to \Bbb R^2$ given by $f(t) = (t^2,t^3)$ is an immersion at $0$.

What is the Derivative of a Vector Field in a Manifold?

Are diffeomorphisms dense in $C^0(M)$ for a compact manifold M?

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