A Continuous Path of Singular Masas in the Hyperfinite II_1 Factor

Abstract

Using methods of R.J.Tauer we exhibit an uncountable family of singular masas in the hyperfinite ${\text{II}}_1$ factor $\mathbb{R}$ all with Pukánszky invariant $\{1\}$, no pair of which are conjugate by an automorphism of $R$. This is done by introducing an invariant $\Gamma (A)$ for a masa $A$ in a \IIi factor $N$ as the maximal size of a projection $e\in A$ for which $Ae$ contains non-trivial centralising sequences for $eNe$. The masas produced give rise to a continuous map from the interval $[0,1]$ into the singular masas in $\mathbb{R}$ equiped with the $d_{\infty ,2}$-metric. A result is also given showing that the Pukánszky invariant is $d_{\infty ,2}$-upper semi-continuous. As a consequence, the sets of masas with Pukánszky invariant $\{n\}$ are all closed.

18 pages

References in corpus (1)

• Values of the Pukanszky Invariant in McDuff Factors

Cited by in corpus (1)

• Values of the Pukanszky Invariant in McDuff Factors