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

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

2009-02-01

arxiv.org/abs/0902.0174v2

Mathematics

Dynamical Systems

14 pages. This version corrects minor errors

Scientific paper

Previous work introduced two measure-conjugacy invariants: the $f$-invariant (for actions of free groups) and $\Sigma$-entropy (for actions of sofic groups). The purpose of this paper is to show that the $f$-invariant is a special case of $\Sigma$-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.

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