Title: A Boolean action of C(M,U(1)) without a spatial model and
a re-examination of the Cameron-Martin theorem

Justin Moore (Cornell Univ.)

Abstract: We will demonstrate that if M is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which preserves the measure and yet does not admit a point realization in the sense of Mackey. This is achieved by exhibiting a strong form of ergodicity of the Boolean action known as whirlyness. This contrasts Mackey's point realization theorem for locally compact second countable groups which asserts that any measure preserving Boolean action of a locally compact second countable group on a separable probability algebra can be realized as an action on the points of a probability space. In the course of proving the main theorem, we will prove some results concerning the infinite dimensional Gaussian measure space (C^N,γ_∞) which contrasts the Cameron-Martin Theorem. This is joint work with Slawomir Solecki.