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Pré-Publication, Document De Travail Année : 2015

Definably amenable NIP groups

Artem Chernikov
  • Fonction : Auteur
  • PersonId : 880593
Pierre Simon
  • Fonction : Auteur
  • PersonId : 958693

Résumé

We study definably amenable NIP groups. We develop a theory of generics, showing that various definitions considered previously coincide, and study invariant measures. Applications include: characterization of regular ergodic measures, a proof of the conjecture of Petrykowski connecting existence of bounded orbits with definable amenability in the NIP case, and the Ellis group conjecture of Newelski and Pillay connecting the model-theoretic connected component of an NIP group with the ideal subgroup of its Ellis enveloping semigroup.

Dates et versions

hal-01134431 , version 1 (23-03-2015)

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Artem Chernikov, Pierre Simon. Definably amenable NIP groups. 2015. ⟨hal-01134431⟩
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