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.
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Develops cube structures on the universal minimal system to study nilsystems, giving alternative proofs for saturation properties and a new algebraic proof that RP^[d] is an equivalence relation even for d=1.
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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.
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Cube structures of the universal minimal system, nilsystems and applications
Develops cube structures on the universal minimal system to study nilsystems, giving alternative proofs for saturation properties and a new algebraic proof that RP^[d] is an equivalence relation even for d=1.