Groups, Geometry, and Dynamics
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Published online: 2010-06-16
The ergodic theory of free group actions: entropy and the f-invariantLewis Bowen (1) The University of Texas at Austin, USA
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.
Keywords: Free groups, entropy, f-invariant
Bowen Lewis: The ergodic theory of free group actions: entropy and the f-invariant. Groups Geom. Dyn. 4 (2010), 419-432. doi: 10.4171/GGD/89