List questions from smooth-manifolds

Published on 28 Mar 2026 - 12:38

29

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What's a smooth neighborhood? Why can it result from a transition map?

Published on 20 Oct 2018 - 17:13

66

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on the Cartan formula, how evaluate the contraction operator $i_{v}$?

Published on 20 Oct 2018 - 19:34

187

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Characteristic classes of unit sphere bundle

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120

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Characteristic classes of exotic 4-manifolds

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168

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Smooth Urysohn function having $0$ as regular value

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Show that a 2x2 matrix group is a Lie Group

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578

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Are these conditions equivalent to the definition of regular coordinate ball?

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26

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What does $S=\{t \in I : \gamma(t)=\gamma'(t) \}$ closed in $I$ by continuity mean? Why is it different from $S$ being a open set?

Published on 22 Oct 2018 - 19:46

54

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Twisty cross notation

Published on 23 Mar 2026 - 9:09

440

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Showing a vector field on the unit quaternions is invariant under left translation action

Published on 28 Mar 2026 - 3:30

154

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Extension of vector field implies extension of function

Published on 26 Mar 2026 - 4:52

411

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Determining whether $y^2=x(x-1)^2$ is an immersed submanifold

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62

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Function that are not smooth because $f(U) \not \subset V$

Published on 26 Mar 2026 - 12:13

75

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Constructing smooth embedding of $M\subseteq \mathbb{R}^n$ into $\mathbb{R}^{n-1}$.

Published on 21 Mar 2026 - 18:12

List Question

Time-dependent manifolds

What's a smooth neighborhood? Why can it result from a transition map?

on the Cartan formula, how evaluate the contraction operator $i_{v}$?

Characteristic classes of unit sphere bundle

Characteristic classes of exotic 4-manifolds

Smooth Urysohn function having $0$ as regular value

Show that a 2x2 matrix group is a Lie Group

Are these conditions equivalent to the definition of regular coordinate ball?

What does $S=\{t \in I : \gamma(t)=\gamma'(t) \}$ closed in $I$ by continuity mean? Why is it different from $S$ being a open set?

Twisty cross notation

Showing a vector field on the unit quaternions is invariant under left translation action

Extension of vector field implies extension of function

Determining whether $y^2=x(x-1)^2$ is an immersed submanifold

Function that are not smooth because $f(U) \not \subset V$

Constructing smooth embedding of $M\subseteq \mathbb{R}^n$ into $\mathbb{R}^{n-1}$.

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