Submission date: 15 February 2015.

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.

Mathematics Subject Classification: 03C45, 37B05, 03C60, 03C64, 22F10, 28D15

Keywords and phrases:

Full text arXiv 1502.04365: pdf, ps.