Timeline for Model geometry uniqueness
Current License: CC BY-SA 4.0
6 events
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| Jun 11, 2021 at 13:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 12, 2021 at 16:46 | comment | added | YCor | If $G$ is any closed subgroup of isometries of the Euclidean space $\mathbf{R}^n$ containing the group $\mathbf{R}^n$ of translations, and $\Gamma=\mathbf{Z}^n$ is the group of integral translations, and $H$ the stabilizer of $0$ in $G$, then the $n$-torus can be viewed as $\Gamma\backslash G/H$. Thus $G$ is far from unique. | |
| May 12, 2021 at 12:21 | answer | added | Vladimir47 | timeline score: 1 | |
| Mar 10, 2020 at 15:32 | comment | added | YCor | 2) if $M$ is not oriented then $G$ can't be chosen connected. The point is not that $G$ acts transitively, but that $G$ includes the $\pi_1(M)$-action on the universal covering of $M$. Even among oriented cases, $G$ connected would miss some cases, e.g., in type $\mathbf{E}^1\times\mathbf{H}^2$. 3) Among the eight 3-dimensional Thurston geometries, the locally symmetric ones are the constant curvature ones, and this are only three among those eight. | |
| Mar 10, 2020 at 15:30 | history | edited | YCor | CC BY-SA 4.0 |
fixed typos
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| Mar 10, 2020 at 15:14 | history | asked | Ian Gershon Teixeira | CC BY-SA 4.0 |