Timeline for Applications of n-dimensional crystallographic groups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 26, 2021 at 17:17 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Mar 29, 2013 at 21:13 | comment | added | Alain Valette | This is more of an application of Bieberbach's theorems: in the proof of quasi-isometric rigidity of $\mathbb{Z}^n$ given in that paper: arxiv.org/abs/math/0509527 it is proved that a group $G$ quasi-isometric to $\mathbb{Z}^n$ admits a proper isometric action on some (finite-dimensional) Euclidean space. By Bieberbach, the group $G$ is virtually abelian, so contains a $\mathbb{Z}^m$ of finite index. Finally $m=n$ by invariance of growth under quasi-isometry. | |
| Mar 27, 2013 at 15:08 | history | edited | Qfwfq | CC BY-SA 3.0 |
deleted 23 characters in body
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| Mar 26, 2013 at 13:17 | answer | added | Ralph | timeline score: 5 | |
| Mar 26, 2013 at 10:38 | answer | added | Dietrich Burde | timeline score: 10 | |
| Mar 11, 2013 at 7:09 | answer | added | Jeff Harvey | timeline score: 5 | |
| Mar 11, 2013 at 4:30 | history | edited | Gerry Myerson | CC BY-SA 3.0 |
typos
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| Mar 11, 2013 at 0:12 | answer | added | Ian Agol | timeline score: 6 | |
| Mar 10, 2013 at 22:38 | comment | added | Misha | It depends on what you mean by "application": I could argue that theory of semisimple Lie group and symmetric spaces is application of affine Coxeter groups since these are equivalent to root systems. | |
| Mar 10, 2013 at 22:34 | history | asked | Qfwfq | CC BY-SA 3.0 |