Definably amenable NIP groups
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.
Cite
@article{arxiv.1502.04365,
title = {Definably amenable NIP groups},
author = {Artem Chernikov and Pierre Simon},
journal= {arXiv preprint arXiv:1502.04365},
year = {2017}
}
Comments
The introduction was reworked to make it more accessible to the general mathematical audience; the argument in Proposition 3.15 was clarified; discussion of the unique ergodicity was moved to Section 3.4, Section 4 now has no subsections; minor presentation improvements and clarifications were made throughout the article; accepted to the Journal of the American Mathematical Society