JournalsggdVol. 4, No. 3pp. 419–432

The ergodic theory of free group actions: entropy and the <var>f</var>-invariant

  • Lewis Bowen

    The University of Texas at Austin, USA
The ergodic theory of free group actions:  entropy and the <var>f</var>-invariant cover
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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 <var>f</var>-invariant. Groups Geom. Dyn. 4 (2010), no. 3, pp. 419–432

DOI 10.4171/GGD/89