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

Lewis Bowen

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arXiv · 0902.0174

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

Lewis Bowen

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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 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.

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BibTeX RIS

Lewis Bowen. 2009-07-13. The ergodic theory of free group actions: entropy and the f-invariant. https://arxiv.org/abs/0902.0174

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