Timeline for Normalizer of the group of segment $C^\infty$ diffeomorphisms in the group of segment homeomorphisms
Current License: CC BY-SA 4.0
14 events
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| Dec 9, 2023 at 15:56 | comment | added | Denis T | Filipkiewicz proved in "Isomorphisms between diffeomorphism groups", 1982, that every isomorphism (as abstract groups) between $Diff^k(M)$ and $Diff^k(N)$ is induced by a $C^k$-diffeo between $M$ and $N$, if $1 \leq k \leq \infty$ and $M, N$ are paracompact manifolds without boundary. So, I think, the problem reduces to finding normaliser of $Diff([0, 1])$ inside $Diff((0, 1))$, which should be known. | |
| Dec 9, 2023 at 9:21 | history | edited | YCor | CC BY-SA 4.0 |
resumed C-infty assumption removed in Todd Trimble's (useful) edit
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| Dec 9, 2023 at 9:17 | comment | added | YCor | I guess it comes from the question of determining the automorphism group of $\mathrm{Diff}^\infty([0,1])$ as Rubin spatiality theorems might reduce to determining this normalizer. I guess it's not trivial and one shouldn't expect a too easy answer. | |
| Dec 9, 2023 at 7:23 | history | edited | YCor |
edited tags
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| Dec 9, 2023 at 7:14 | comment | added | Henry | Tranks a lot for changing title and text. It is perfectly precise now. | |
| Dec 9, 2023 at 2:08 | history | edited | Todd Trimble | CC BY-SA 4.0 |
clarified title and question
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| Dec 9, 2023 at 0:03 | comment | added | tj_ | The question is interesting. Maybe you could change the notaion (and title), because usually $C^0[0,1]$ refers to the continuous, real-valued functions on $[0,1]$ and not to the homeomorphisms of $[0,1]$ and similar for $C^\infty$. | |
| Dec 8, 2023 at 23:32 | comment | added | Dieter Kadelka | You should make your question much more explicit. Otherwise it will be closed, I think. | |
| Dec 8, 2023 at 21:36 | comment | added | Henry | It refers to only the homeprphisms and smooth diffeomorphisms, respectively, with composition as the group multiplication. | |
| Dec 8, 2023 at 13:48 | review | Close votes | |||
| Dec 15, 2023 at 3:06 | |||||
| Dec 8, 2023 at 12:48 | comment | added | Dieter Kadelka | What is the (not commutative) group structure of $C^0[0,1]$? | |
| Dec 8, 2023 at 12:48 | review | Low quality posts | |||
| Dec 9, 2023 at 2:11 | |||||
| S Dec 8, 2023 at 12:21 | review | First questions | |||
| Dec 9, 2023 at 19:36 | |||||
| S Dec 8, 2023 at 12:21 | history | asked | Henry | CC BY-SA 4.0 |