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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 II1\rm{II}_{1} factor whose \emph{left-right-measure} is the class of Lebesgue measure. We show that for each subset SβŠ†NS\subseteq \mathbb{N}, there exist uncountably many pairwise non conjugate singular masas in the free group factors with \emph{Puk\'{a}nszky invariant} Sβˆͺ{∞}S\cup\{\infty\}.Comment: 24 pages, to appear in Houston. J. Mat

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