Groups, Geometry, and Dynamics


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Volume 4, Issue 3, 2010, pp. 419–432
DOI: 10.4171/GGD/89

Published online: 2010-06-16

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

Lewis Bowen[1]

(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