Timeline for Are there uniformly discrete paradoxical subsets in $\mathbb{R}^3$?
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| Jul 15, 2013 at 18:28 | comment | added | Terry Tao | Great! So one can probably classify all the possible isometry semigroups of uniformly discrete sets using this, though there is still the problem of ensuring that such semigroups are finitely generated... of course to avoid degeneracies one should assume that the uniformly discrete set is not contained in a hyperplane. It might be fun to work out exactly what the answer is here, though I don't think I'll have the time to think about it myself... | |
| Jul 15, 2013 at 6:10 | comment | added | user6976 | @Terry: There is an analogue of Gromov polynomial growth theorem for semigroups with cancelation ($xy=xz\to y=z$, $yx=zx\to y=z$), see Grigorchuk, R. I. Semigroups with cancellations of degree growth. Mat. Zametki 43 (1988), no. 3, 305--319, 428; translation in Math. Notes 43 (1988), no. 3-4, 175–183 | |
| Jul 14, 2013 at 21:14 | vote | accept | Alexander Pruss | ||
| Jul 14, 2013 at 20:04 | history | edited | Terry Tao | CC BY-SA 3.0 |
added 34 characters in body
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| Jul 14, 2013 at 19:55 | history | answered | Terry Tao | CC BY-SA 3.0 |