The ergodic theory of free group actions: entropy and the f-invariant

Abstract

Previous work introduced two measure-conjugacy invariants: the f-invariant (for actions of free groups) and -entropy (for actions of sofic groups). The purpose of this paper is to show that the f-invariant is a special case of -entropy. There are two applications: the f-invariant is invariant under group automorphisms and there is a uniform lower bound on the f-invariant of a factor in terms of the original system.