Timeline for Gromov's pseudogroups and Tao's approximate groups
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2018 at 5:14 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
added projecteuclid link
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| Oct 23, 2016 at 14:04 | answer | added | Igor Belegradek | timeline score: 7 | |
| Oct 23, 2016 at 7:20 | history | edited | Mikhail Katz |
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| Oct 22, 2016 at 17:43 | comment | added | Mikhail Katz | @IgorBelegradek, can you format this as an answer? Also, Breuillard et al don't comment on pseudogroups. | |
| Oct 21, 2016 at 9:49 | history | edited | Mikhail Katz |
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| Oct 21, 2016 at 0:23 | comment | added | Igor Belegradek | I don't know enough about approximate groups to give a full-blown answer but I think pseudogroups (in Gromov's sense) and approximate groups are different techniques that sometimes achieve the same goals, such as the Margulis lemma and its consequences. This is explained in front.math.ucdavis.edu/1110.5008. I think the point is that if one only cares about group theoretic conclusions (e.g. that a certain fundamental group is virtually nilpotent), then one can ignore the space where the local preudogroup acts and focus on suitable group theoretic data. | |
| Oct 20, 2016 at 21:25 | review | Close votes | |||
| Oct 20, 2016 at 23:57 | |||||
| Oct 20, 2016 at 17:12 | comment | added | john mangual | it is also connection to additive number theory as the nilsequences come from nilpotent lie group. he is also discussing the word problem on rotation groups | |
| Oct 20, 2016 at 17:05 | comment | added | Mikhail Katz | @johnmangual, that's the connection to geometric group theory, and also to his (harder) theorem on groups of polynomial growth. | |
| Oct 20, 2016 at 17:04 | comment | added | john mangual | Oh wow! His example of $\epsilon$-flat manifolds are nil-manifolds! | |
| Oct 20, 2016 at 16:18 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
added 272 characters in body
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| Oct 20, 2016 at 14:54 | answer | added | john mangual | timeline score: 3 | |
| Oct 20, 2016 at 14:25 | comment | added | HJRW | I'm not aware of any conceptual relationship between them. Why should one exist? Hopefully not just because of the names... | |
| Oct 20, 2016 at 14:21 | comment | added | john mangual | One is in differential geometry and the other is in additive combinatorics -- so I am not sure there will be any relation at all. And yet, Tao is known to take certain cues from Gromov at times (both of whom are still alive, active and occasionally appear on here). | |
| Oct 20, 2016 at 8:22 | history | asked | Mikhail Katz | CC BY-SA 3.0 |