Question

How to prove that $\frac{d}{dt}|_{t=t_0}(\theta_t^A)_p=(\theta_{t_0}^(\mathscr{L}_VA))_p$, 12.36 in Lee's Introduction to Smooth Manifolds

score 122 · Answer 1 · 2026-03-26 01:12:39

122

Views

How to prove that $\frac{d}{dt}|_{t=t_0}(\theta_t^A)_p=(\theta_{t_0}^(\mathscr{L}_VA))_p$, 12.36 in Lee's Introduction to Smooth Manifolds

Published on 26 Mar 2026 - 1:12

score 628 · Answer 2 · 2026-03-28 14:44:25

628

Views

smooth vector field on a manifold and smooth vector field on a open subset of a manifold

Published on 28 Mar 2026 - 14:44

score 799 · Answer 3 · 2026-03-28 05:59:29

799

Views

About degree of a smooth map between Manifolds

Published on 28 Mar 2026 - 5:59

score 206 · Answer 4 · 2019-10-16 18:42:51

206

Views

Symmetry of Fubini Theorem versus Skew Symmetry of 2-forms

Published on 16 Oct 2019 - 18:42

score 349 · Answer 5 · 2026-03-26 15:17:16

349

Views

Self Intersection mod 2 of Central curve on Möbius band

Published on 26 Mar 2026 - 15:17

score 789 · Answer 6 · 2019-10-17 07:43:06

789

Views

What's an example where the inclusion map $\iota: A \to B$ is smooth and a topological embedding but not an immersion?

Published on 17 Oct 2019 - 7:43

score 68 · Answer 7 · 2026-03-26 01:16:37

68

Views

Show that $((0,1)\times(0,1))\cup(\{1\}\times[0,1])$ is not a smooth manifold with boundary$

Published on 26 Mar 2026 - 1:16

score 58 · Answer 8 · 2019-10-17 22:43:07

58

Views

Isomorphism between homology groups if we throw away some submanifold from the interior

Published on 17 Oct 2019 - 22:43

score 55 · Answer 9 · 2019-10-18 17:53:17

55

Views

The invertability of a differential and it's matrix representation

Published on 18 Oct 2019 - 17:53

score 81 · Answer 10 · 2026-03-28 10:40:45

81

Views

Isomorphisms of vector bundles preserve orientability

Published on 28 Mar 2026 - 10:40

score 488 · Answer 11 · 2026-03-28 10:40:42

488

Views

Vector bundle orientable if and only if determinant bundle is (Bott and Tu Prop. 11.4)

Published on 28 Mar 2026 - 10:40

score 80 · Answer 12 · 2026-04-02 13:06:05

80

Views

Is the set where there is a unique distance minimizer to a submanifold open?

Published on 02 Apr 2026 - 13:06

score 142 · Answer 13 · 2019-10-20 12:39:32

142

Views

hypersurface, manifold

Published on 20 Oct 2019 - 12:39

score 391 · Answer 14 · 2019-10-20 15:24:20

391

Views

Integration over parametrizations in the border of a manifold with corners (John M. Lee Introduction to Smooth Manifolds exercise 16.22)

Published on 20 Oct 2019 - 15:24

score 518 · Answer 15 · 2026-03-25 16:00:28

518

Views

Understanding Morse homology with the example of a circle

Published on 25 Mar 2026 - 16:00

List Question

How to prove that $\frac{d}{dt}|_{t=t_0}(\theta_t^A)_p=(\theta_{t_0}^(\mathscr{L}_VA))_p$, 12.36 in Lee's Introduction to Smooth Manifolds

smooth vector field on a manifold and smooth vector field on a open subset of a manifold

About degree of a smooth map between Manifolds

Symmetry of Fubini Theorem versus Skew Symmetry of 2-forms

Self Intersection mod 2 of Central curve on Möbius band

What's an example where the inclusion map $\iota: A \to B$ is smooth and a topological embedding but not an immersion?

Show that $((0,1)\times(0,1))\cup(\{1\}\times[0,1])$ is not a smooth manifold with boundary$

Isomorphism between homology groups if we throw away some submanifold from the interior

The invertability of a differential and it's matrix representation

Isomorphisms of vector bundles preserve orientability

Vector bundle orientable if and only if determinant bundle is (Bott and Tu Prop. 11.4)

Is the set where there is a unique distance minimizer to a submanifold open?

hypersurface, manifold

Integration over parametrizations in the border of a manifold with corners (John M. Lee Introduction to Smooth Manifolds exercise 16.22)

Understanding Morse homology with the example of a circle

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