On free-group algorithms that sandwich a subgroup between free-product factors

On the Nilpotent Multiplier of a Free Product

Finite Free Entropy and Free Group Factors

We show the existence of noncommutative random variables with finite free entropy but which do not generate a free group factor. In particular, this gives an example of variables X1, . . . , Xn such that δ(X1, . . . , Xn) = n while W ∗(X1, . . . , Xn) ≇ L(Fn).

Interpolated Free Group Factors

The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free products, algebraic techniques are developed which allow us to show R∗R ∼= L(F2) where R is the hyperfinite II1–fac...

Finite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup that is locally free but not free

The purpose of this note is to show that the collection LF of finite volume hyperbolic 3-manifolds whose fundamental groups contain a subgroup that is locally free but not free is commensurably infinite. This result is stated formally as Theorem 4.1, and gives a strong answer to a question of Kropholler given in the Problem List in Niblo and Roller [19]. Recall that two hyperbolic 3-manifolds N...

On Ozawa’s Property for Free Group Factors

We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra Q of a free group factor LFn, 2 ≤ n ≤ ∞ has relative commutant diffuse (i.e. without atoms), then Q is amenable.