Seminar 2.5.15 Seward

Speaker: Brandon Seward

Title: Krieger’s finite generator theorem for ergodic actions of countable groups

Abstract: The classical Krieger finite generator theorem states that if a free ergodic probability-measure-preserving action of Z has entropy less than log(k), then the action admits a generating partition consisting of k sets. This was extended to actions of amenable groups independently by Rosenthal and Danilenko–Park. We introduce the notion of Rokhlin entropy which is defined for actions of general countable groups. Rokhlin entropy may be viewed as a natural extension of classical entropy, as when the acting group is amenable the two notions coincide. Using this notion of entropy, we prove Krieger’s finite generator theorem for actions of general countable groups.