Definable Topological Dynamics in Metastable Theories

Abstract

We initiate a study of the definable topological dynamics of groups definable in metastable theories. In stable theories, it is known that the quotient of a group G by its type-definable connected component G00 is isomorphic to the Ellis Group of the flow (G(M),SG(M)); we consider whether these results could be extended to the broader metastable setting. Further, the definable topological dynamics of compactly dominated groups in the o-minimal setting is well understood. We investigate to what extent stable domination is a suitable analogue of compact domination in regards to describing the Ellis Group of metastable definable groups