The Laplacian MASA in a free group factor
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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 δ(B) = 1. This is achieved by proving that the conditional expectation double struct E signBonto 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.