Timeline for Must a surjective infinitesmal isometry between simply connected spaces be injective? [duplicate]
Current License: CC BY-SA 4.0
17 events
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| Mar 14, 2023 at 0:28 | comment | added | Moishe Kohan | Yes, you are missing the simple fact that the only biholomorphic automorphisms of the complex plane are linear and the functions in the linked question are definitely not. You can also read my linked answer to the MSE question where lack of injectivity is immediate from the construction. | |
| Mar 13, 2023 at 22:24 | history | closed |
Moishe Kohan CommunityBot |
Duplicate of Surjective entire functions without critical points | |
| Mar 13, 2023 at 22:11 | comment | added | Amr | @MoshieKohan The link mathoverflow.net/questions/147110/… which you gave does answer my question provided I can also see that the functions of your link are not injective. I am trying to figure that out myself but maybe I am missing something | |
| Mar 13, 2023 at 22:05 | review | Close votes | |||
| Mar 13, 2023 at 22:26 | |||||
| Mar 13, 2023 at 21:58 | comment | added | Moishe Kohan | Here is an MSE question of the same nature: math.stackexchange.com/questions/553299/… | |
| Mar 13, 2023 at 21:49 | answer | added | Neal | timeline score: 0 | |
| Mar 13, 2023 at 21:40 | comment | added | Wojowu | @AntonPetrunin That's why I am defining M to be an open subset of this double cover. Say you can remove one line segment from it. (that was for the original version of the question) | |
| Mar 13, 2023 at 21:36 | comment | added | Amr | @MoisheKohan Can you please give me the math exchange link , and I will delete this question | |
| Mar 13, 2023 at 21:34 | comment | added | Moishe Kohan | It was asked numerous times at MSE. The answer is always negative. | |
| Mar 13, 2023 at 21:23 | history | edited | Amr | CC BY-SA 4.0 |
Added a surjectivity hypothesis
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| Mar 13, 2023 at 21:09 | comment | added | Amr | @AntonPetrunin Ahh, I think I see. Sorry to bother you with more questions, but what would happen if I also required the map $f$ in my question to be surjective ? | |
| Mar 13, 2023 at 21:04 | comment | added | Anton Petrunin | Use Whitney theorem to embed $\mathbb{R}\mathrm{P}^2$ into $\mathbb{R}^5$, the rest should be clear. | |
| Mar 13, 2023 at 20:57 | comment | added | Amr | @AntonPetrunin Thank you for your comments, I am sorry I still cant wrap my head around your example, can you please write it with more clarification as an answer? | |
| Mar 13, 2023 at 20:49 | comment | added | Anton Petrunin | Fixing problem in Wojowu's suggestion: Consider double cover of a tubular neighborhood of a projective plane embedded into a euclidean space. | |
| Mar 13, 2023 at 20:46 | comment | added | Anton Petrunin | @Wojowu double cover of an annulus is not simply-connected. | |
| Mar 13, 2023 at 20:08 | comment | added | Wojowu | Let $N$=plane, $M'\subseteq N$ some annulus, and $M$=an open subset of a double cover of $M'$ which is simply connected and doesn't inject onto $M'$. | |
| Mar 13, 2023 at 20:02 | history | asked | Amr | CC BY-SA 4.0 |