AN EXAMPLE OF A PROPERTY Γ FACTOR WITH COUNTABLE FUNDAMENTAL GROUP

SORIN POPA

Abstract. We construct a class of examples of type II_{1} factors with the property Γ of Murray and von Neumann but countable fundamental group. These factors do not contain any infinite dimensional property T factors and cannot be embedded into free group factors either. For the construction, we use the rigidity of the embedding ℤ^{2} ⊂ Z^{2} ⋊ SL(2, ℤ), some perturbation results for algebras that are uniformly close, and a recent result of Gaboriau on cost of measured equivalence relations implemented by SL(2, ℤ).