The ergodic theory of free group actions: entropy and the -invariant
Lewis Bowen
The University of Texas at Austin, USA
![The ergodic theory of free group actions: entropy and the $f$-invariant cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-4-issue-3.png&w=3840&q=90)
Abstract
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. 419–432
DOI 10.4171/GGD/89