Singular Masas and Measure-Multiplicity Invariant

Abstract

In this paper we study relations between the \emph{left-right-measure} and properties of singular masas. Part of the analysis is mainly concerned with masas for which the \emph{left-right-measure} is the class of product measure. We provide examples of Tauer masas in the hyperfinite ${\mathrm{II}}_1$ factor whose \emph{left-right-measure} is the class of Lebesgue measure. We show that for each subset $S\subseteq \mathbb{N}$, there exist uncountably many pairwise non conjugate singular masas in the free group factors with \emph{Pukánszky invariant} $S\cup \{\infty \}$.

24 pages, to appear in Houston. J. Math