Timeline for Local diffeomorphism on a neighborhood of an embedding
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| May 14, 2019 at 6:42 | comment | added | Jan Vysoky | Thank you. In the end, I have kind of combined your approach with the one in the lecture notes I have posted (I mostly tried to avoid tubular neighborhoods as I am not completely unfailing in their understanding :)). I learned about compact exhaustions along the way (nice thing!). This is where I have to stop and return to the original paper :) Thank you for your help. | |
| May 13, 2019 at 6:57 | comment | added | Pavel | P.S. Have a look at the proof of the tubular neighborhood theorem (Theorem 10.19) in J.M.Lee's Introduction to smooth manifolds. Perhaps a similar idea can be used to prove the proposition above without using exhaustions. | |
| May 13, 2019 at 6:19 | comment | added | Pavel | Yes, the result is definitively not new and the compact exhaustion is a standard trick. It probably can not be done much better. | |
| May 13, 2019 at 5:46 | comment | added | Jan Vysoky | I have found a reference with a very similar ideas here: staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/… | |
| May 11, 2019 at 10:41 | history | edited | Pavel | CC BY-SA 4.0 |
added 2 characters in body
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| May 11, 2019 at 10:30 | history | edited | Pavel | CC BY-SA 4.0 |
edited body
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| May 11, 2019 at 10:22 | history | edited | Pavel | CC BY-SA 4.0 |
Generalization of Lemma 2
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| May 11, 2019 at 10:06 | history | edited | Pavel | CC BY-SA 4.0 |
added 206 characters in body; added 8 characters in body
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| May 11, 2019 at 9:24 | comment | added | Jan Vysoky | Wow, thanks for the updated version. I won't get to it during the weekend, but I will check it as soon as possible. | |
| May 11, 2019 at 8:56 | history | edited | Pavel | CC BY-SA 4.0 |
non-compact version holds too
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| May 10, 2019 at 21:36 | comment | added | Jan Vysoky | Yeah, I also think it is not important, that is why added this separately. However, it is entirely possible that the statement holds only for the particular $\mathcal{V}$ they are considering (although I don't think so), so it does not hold in full generality... | |
| May 10, 2019 at 21:20 | comment | added | Pavel | Btw., I think that 3) is irrelevant because you can always shrink E to a tubular neighborhood $T$of $\nu(N)$ and set $F=\nu^{-1}(T)$. | |
| May 10, 2019 at 21:06 | vote | accept | Jan Vysoky | ||
| May 10, 2019 at 21:00 | comment | added | Pavel | Ah, I see, I misunderstood "closed". | |
| May 10, 2019 at 20:57 | comment | added | Jan Vysoky | That is very nice, thank you! I understand why you need compactness in your proof, and I see not way around this at first glance. Unfortunately, I need it without this restriction - but I will definitely take note of your approach, thanks. | |
| May 10, 2019 at 20:45 | history | edited | Pavel | CC BY-SA 4.0 |
added 37 characters in body
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| May 10, 2019 at 20:35 | history | answered | Pavel | CC BY-SA 4.0 |