Previous work introduced two measure-conjugacy invariants: the f-invariant (for actions of free groups) and Σ-entropy (for actions of sofic groups). The purpose of this paper is to show that the f-invariant is essentially a special case of Σ-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.
Cite this article
Lewis Bowen, The ergodic theory of free group actions: entropy and the -invariant. Groups Geom. Dyn. 4 (2010), no. 3, pp. 419–432DOI 10.4171/GGD/89