Definably amenable NIP groups

Artem Chernikov; Pierre Simon

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arXiv · 1502.04365

Definably amenable NIP groups

Artem Chernikov·Pierre Simon

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Abstract

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.

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Artem Chernikov, Pierre Simon. 2015-02-15. Definably amenable NIP groups. https://arxiv.org/abs/1502.04365

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