Topological dynamics and definable groups

TL;DR

This paper explores the connection between topological dynamics and definable groups, demonstrating that Ellis theory applied to fsg groups in NIP theories yields the quotient G/G^00.

Contribution

It extends the understanding of the relationship between abstract topological dynamics and stable group theory in the context of NIP theories.

Findings

Ellis theory applied to G(M) yields G/G^00

Provides new insights into the structure of definable groups in NIP theories

Connects topological dynamics with model-theoretic group quotients

Abstract

Following the works of Newelski we continue the study of the relations between abstract topological dynamics and generalized stable group theory. We show that the Ellis theory, applied to the action of G(M) on its type space, for G an fsg group in a NIP theory, and M any model, yields the quotient G/G^00.