Algebraic characterization of RP^[d] via new topology and proof that order d-1 maximal factors are topological characteristic factors for higher-order configurations in group actions.
Infinite sumsets in $U^k(\Phi)$-uniform sets
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abstract
Extending recent developments of Kra, Moreira, Richter and Roberson, we study infinite sumset patterns in $U^k(\Phi)$-uniform subsets of the integers, defined via the local uniformity seminorms introduced by Host and Kra. We relate the degree $k$ of a $U^k(\Phi)$-uniform set to the existence of a rich variety of sumset patterns. As a counterpart, we stablish higher order parity obstruction to sumsets arising from nilsystems. We also provide examples of $U^k(\Phi)$-uniform sets for applications, including sets arising from the Thue-Morse and Rudin-Shapiro sequences.
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math.DS 1years
2026 1verdicts
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On higher order regionally proximal relations and topological characteristic factors for group actions
Algebraic characterization of RP^[d] via new topology and proof that order d-1 maximal factors are topological characteristic factors for higher-order configurations in group actions.