Conjugacy equivalence relation on subgroups

Abstract

Abstract. If G is a countable group containing a copy of F 2 then the conjugacy equivalence relation on subgroups of G attains the maximal possible complexity.

Superrigidity and countable Borel equivalence relations

“…If we identify F 2 with a suitably chosen group of recursive permutations of N, then we see that E ∞ may be realized as a subset of ≡ T . Thus the following conjecture of Hjorth [3] implies that ≡ T is universal.…”

Countable Borel Equivalence Relations

“…Now, if we identify F 2 with a suitably chosen group of recursive permutations of N, we see that E ∞ may be realized as a subset of ≡ T . Thus the following conjecture of Hjorth [3] would imply that ≡ T is universal.…”

Universal Borel actions of countable groups

“…Theorem 3.7 (Andretta-Camerlo-Hjorth [1]). If the countable group G has a free nonabelian subgroup, then ≈ G is countable universal.…”