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arXiv · 1909.11349

Strictly ergodic distal models and a new approach to the Host-Kra factors

Yonatan Gutman·Zhengxing Lian
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Abstract

Cocycles are a key object in Antol\'{i}n Camarena and Szegedy's (topological) theory of nilspaces. We introduce measurable counterparts, named nilcycles, enabling us to give conditions which guarantee that an ergodic group extension of a strictly ergodic distal system admits a strictly ergodic distal topological model, revisiting a problem studied by Lindenstrauss. In particular we show that if the base space is a dynamical nilspace then a dynamical nilspace topological model may be chosen for the extension. This approach combined with a structure theorem of Gutman, Manners and Varj\'{u} applied to the ergodic group extensions between successive Host-Kra characteristic factors gives a new proof that these factors are inverse limit of nilsystems.

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Yonatan Gutman, Zhengxing Lian. 2019-09-25. Strictly ergodic distal models and a new approach to the Host-Kra factors. https://doi.org/10.1016/j.jfa.2022.109779

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