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SUMMARY:The structure of cubespaces attached to minimal distal dynamical s
 ystems - Yonatan Gutman (IHES)
DTSTART:20120224T160000Z
DTEND:20120224T170000Z
UID:TALK35007@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:Cubespaces were recently introduced by Camarena and B. Szegedy
 . These\nare compact spaces X together with closed collections of "cubes"\
 n'C^{n}(X)\\subset X^{2^{n}}\, n=1\,2\,.... verifying some natural\naxioms
 . \n\n\nWe investigate cubespaces induced by minimal dynamical\ntopologica
 l systems $(G\,X)$ where $G$ is Abelian. Szegedy-Camarena's\nDecomposition
  Theorem furnishes us with a natural family of canonical\nfactors $(G\,X_{
 k})$\, $k=1\,2\,\\ldots$. These factors turn out to be\nmultiple principla
 l bundles.We show that under the assumption that all\nfibers are Lie group
 s $(G\,X_{k})$ is a nilsystem\, i.e. arising from a\nquotient of a nilpote
 nt Lie group.This enable us to give simplified\nproofs to some of the resu
 lts obtained by Host-Kra-Maass in order to\ncharacterize nilsequences inte
 rnally.
LOCATION:MR15\, CMS
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