The structure of cubespaces attached to minimal distal dynamical systems

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• Yonatan Gutman (IHES)
• Friday 24 February 2012, 16:00-17:00
• MR15, CMS.

If you have a question about this talk, please contact Ben Green.

Cubespaces were recently introduced by Camarena and B. Szegedy. These are compact spaces X together with closed collections of “cubes” ‘C^{(X)\subset X}{2^{n}}, n=1,2,.... verifying some natural axioms.

We investigate cubespaces induced by minimal dynamical topological systems $(G,X)$ where $G$ is Abelian. Szegedy-Camarena’s Decomposition Theorem furnishes us with a natural family of canonical factors $(G,X_{k})$, $k=1,2,\ldots$. These factors turn out to be multiple principlal bundles.We show that under the assumption that all fibers are Lie groups $(G,X_{k})$ is a nilsystem, i.e. arising from a quotient of a nilpotent Lie group.This enable us to give simplified proofs to some of the results obtained by Host-Kra-Maass in order to characterize nilsequences internally.

This talk is part of the Discrete Analysis Seminar series.

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