Timeline for Are there multiple conjugacy classes of order 2 elements in the smooth automorphism group of $\mathbb{R}$?
Current License: CC BY-SA 4.0
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| Oct 15, 2019 at 13:10 | history | edited | YCor |
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| Oct 15, 2019 at 13:07 | comment | added | YCor | This is widely known as (smooth) diffeomorphism group. It's true. One way to prove this is to observe that $g$ preserves a Riemannian metric, and then use that every Riemannian manifold that is homeomorphic to $\mathbf{R}$ is smoothly isometric to an interval of $\mathbf{R}$. By the existence of an orientation-reversing involution, it has to be smoothly isometric to $\mathbf{R}$ or $]-1,1[$. One easily concludes. | |
| Oct 15, 2019 at 13:00 | review | First posts | |||
| Oct 15, 2019 at 13:57 | |||||
| Oct 15, 2019 at 12:58 | history | asked | Anon E. Mous | CC BY-SA 4.0 |