Work

Definably amenable NIP groups

Year: 2015

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1502.04365

Authors: Chernikov, Artem, Simon, Pierre

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, European Commission, Agence Nationale de la Recherche

Awards: G1135293650, Model Theory of Unstable Structures, G3207356259, G3498229676, G3602381172, G3633247507, G393177772, Model-Theoretic Classification, Graph Combinatorics, and Topological Dynamics, G4104599821, G459516591, G5702163051, G609738274, Valuations, Combinatorics and Model Theory, G7240651115, Fondation Sciences Mathématiques de Paris, G7376787254, CAREER: Model theory, measures and combinatorics

OpenAlex ID: W4290754530

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