Open Collections

Description

In general orbit equivalence between free measure-preserving actions of countably infinite groups on standard probability measure spaces may not preserve entropy. A few years ago Tim Austin showed that integrable orbit equivalence between actions of finitely generated amenable groups does preserve entropy. I will introduce a notion of Shannon orbit equivalence, weaker than integrable orbit equivalence, and a property SC for actions. The Shannon orbit equivalence between actions of sofic groups with the property SC preserve the maximal sofic entropy. If a group G has a w-normal subgroup H such that H is amenable and not locally virtually cyclic, then every action of G has the property SC. In particular, if two Bernoulli shifts of such a sofic group are Shannon orbit equivalent, then they are conjugate. This is joint work with David Kerr.