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Feb
11
accepted Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
Feb
10
comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
I've actually been looking at this proof at a more careful level. And I realized Tubular Neighborhood and Retraction are exactly the tools that Lee used to solve the question I have. I guess I will choose @Potato as the best answer if nobody gives a better answer in the following couple of days! Thanks man, @Potato!
Feb
9
comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
I saw this proof before. But since I am not aware of Whitney approximation theorem or the smooth retraction mentioned in the proof, I skipped it. Bott, Tu's book's proof requires less background knowledge. But as I explained, I found I can't get around that point. I still wish that someone might be able to tell me how it is possible.
Feb
9
asked Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
Nov
20
awarded  Critic
Nov
20
awarded  Supporter
Nov
15
accepted Confused at the definition for integration of differential form over manifold
Nov
14
asked Confused at the definition for integration of differential form over manifold
Nov
13
comment How to prove this formula for Lie derivative for differential forms
@FlybyNight I believe $\phi_t$ in my notation is the $f$ in your notation. And $\phi_t^* w$, viewed as a whole thing, is exactly the $w^*$ in your notation. $\phi_t^*$ is the mapping that takes $ w$ to $w^*$. But never mind, I know how to prove this thing now. It's only a simple computation once you know what all those mappings really are. Thanks anyway.
Nov
13
revised How to prove this formula for Lie derivative for differential forms
edited body
Nov
13
comment How to prove this formula for Lie derivative for differential forms
@FlybyNight huh? $w$ here is a differential form.
Nov
12
asked How to prove this formula for Lie derivative for differential forms
Sep
26
accepted How do I see that the tangent bundle of torus is trivial
Sep
26
comment How do I see that the tangent bundle of torus is trivial
Thanks, @Neal, for providing so many ways of seeing it
Sep
26
comment How do I see that the tangent bundle of torus is trivial
@RyanBudney Thanks! I guess that's one way of doing it.
Sep
26
comment How do I see that the tangent bundle of torus is trivial
what do you mean by taking one vector field in the direction of each "factor"?
Sep
26
asked How do I see that the tangent bundle of torus is trivial
Sep
10
accepted How to show the height function of a torus has 4 critical points
Sep
10
comment How to show the height function of a torus has 4 critical points
Thank you. I wasn't aware of this form before.
Sep
10
comment How to show the height function of a torus has 4 critical points
Thanks, @t.b.! I will take a look.