Timeline for Hilbert space compression of the lamplighter group
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2018 at 17:58 | comment | added | YCor | PS: since the lamplighter has exponent 1 but does not QI-embed into Hilbert space, this is one witness (among others) that the notion of "Hilbert space compression number" is a poor notion and that the notion of distortion introduced by Gromov, Gersten is a much more versatile one. "Having compression number $1$" can be rephrased as "admits, for every $\varepsilon>0$, a uniform embedding into a Hilbert space with distortion $\preceq n^{1+\varepsilon}$. The latter formulation conveys a more accurate intuition of what it means and how it can be improved. | |
| Nov 11, 2013 at 21:54 | vote | accept | Michal Kotowski | ||
| S Nov 11, 2013 at 20:47 | history | answered | YCor | CC BY-SA 3.0 | |
| S Nov 11, 2013 at 20:47 | history | made wiki | Post Made Community Wiki by YCor |