Timeline for Open subsets of Euclidean space in dimension 5 and higher admitting exotic smooth structures
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2018 at 11:40 | vote | accept | Nautilus | ||
| Mar 16, 2018 at 11:40 | answer | added | Nautilus | timeline score: 2 | |
| Mar 13, 2018 at 16:51 | answer | added | Misha | timeline score: 7 | |
| Sep 26, 2017 at 10:08 | history | edited | Nautilus | CC BY-SA 3.0 |
edit added
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| Sep 26, 2017 at 10:00 | history | edited | Nautilus | CC BY-SA 3.0 |
edit added
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| Sep 26, 2017 at 7:48 | history | edited | Nautilus | CC BY-SA 3.0 |
added 30 characters in body
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| Sep 26, 2017 at 7:29 | history | edited | Nautilus | CC BY-SA 3.0 |
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| Sep 26, 2017 at 5:07 | history | edited | Nautilus | CC BY-SA 3.0 |
more precise formulation
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| Sep 26, 2017 at 4:40 | comment | added | Nautilus | Misha: thank you very much for the useful hint. If i understand it well, what Kirby told you is that there are homeomorphic open subsets of $R^n$, $n\geq 5$, that are not diffeomorphic (each of them endowed with its standard smooth structure). Your expression "are homeomorphic but homeomorphisms are not isotopic to diffeomorphisms" is equivalent to what is written above, but somewhat less clear (a diffeomorphim is a homeomorphism and it is isotopic to itself, thus no diffeomorphism exists). | |
| Sep 25, 2017 at 19:54 | comment | added | Misha | About 10 years ago Rob Kirby told me about an example of open domains in $R^n$, $n\ge 5$, which are homeomorphic but homeomorphisms are not isotopic to diffeomorphisms. Sadly, I do not remember what the examples were. (I noted this in a list of open problems about boundaries of groups compiled at AIM in 2007.) One can ask Rob again, maybe he still remembers. | |
| Sep 25, 2017 at 13:18 | history | edited | Nautilus | CC BY-SA 3.0 |
title rendered more precise
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| Sep 21, 2017 at 5:51 | history | edited | Nautilus | CC BY-SA 3.0 |
more precise formulation
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| Sep 20, 2017 at 22:49 | history | edited | Nautilus | CC BY-SA 3.0 |
improved formatting
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| Sep 20, 2017 at 21:20 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
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| Sep 20, 2017 at 20:28 | history | edited | Nautilus |
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| Sep 20, 2017 at 19:36 | comment | added | Nautilus | Question (2) is raised in mathoverflow.net/questions/114528/… but not answered there. The discussion seems to turn around the known existence of small exotic R4's on one hand, and contractible opens sets on the other. Apriori, the answer could be positive for (1) above and negative for (2). | |
| Sep 20, 2017 at 19:13 | comment | added | j.c. | This question seems to be a duplicate of this one mathoverflow.net/questions/114528/… but I haven't voted to close since your specific question doesn't seem to be answered explicitly there. The comments of Tom Goodwillie and Igor Belegradek seem to state that the answer is no though. | |
| Sep 20, 2017 at 18:41 | history | asked | Nautilus | CC BY-SA 3.0 |