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Journal of the London Mathematical Society Advance Access originally published online on January 31, 2007
Journal of the London Mathematical Society 2007 75(1):243-254; doi:10.1112/jlms/jdl019
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© 2007 London Mathematical Society

A continuous path of singular masas in the hyperfinite II1 factor

Allan Sinclair

School of Mathematics
University of Edinburgh
Edinburgh
EH9 3JZ
United Kingdom
a.sinclair{at}ed.ac.uk

Stuart White

Department of Mathematics
University of Glasgow
Glasgow
G12 8QW
United Kingdom
s.white{at}maths.gla.ac.uk

Using methods of Tauer, we exhibit an uncountable family of singular masas in the hyperfinite II1 factor R all with Pukánszky invariant {1}, no pair of which is conjugate by an automorphism of R. This is done by introducing an invariant {Gamma}(A) for a masa A in a II1 factor N as the maximal size of a projection e{epsilon}A for which A e contains non-trivial centralizing sequences for eN e. The masas produced give rise to a continuous map from the interval [0, 1] into the singular masas in R equipped 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.

2000 Mathematics Subject Classification 46L10 (primary).

Received February 15, 2006; published online January 31, 2007.


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