The ergodic theory of free group actions: entropy and the f-invariant
By Lewis Bowen. 2009
56 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/255eda5e04b037a4b0bc4054e3f80656910c4e3c
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “rem 7.5 that this definition is independent of the choice of generating subalgebra, and in Theorem 9.5 that it agrees with the definition in the case of a topological model. Theorem 6.7 (Theorem 1.3 in [4]). Let (X,µ) be a standard probability space, and Fry(X,µ) by measurepreserving transformations. ”