The Laplacian Masa in a Free Group Factor

The Laplacian (or radial) masa in a free group factor is generated by the sum of the generators and their inverses. We show that such a masa B is strongly singular and has Popa invariant delta(B) = 1. This is achieved by proving that the conditional expectation onto B is an asymptotic homomorphism. We also obtain similar results for the free product of discrete groups, each of which contains an element of infinite order.