## 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 II_{1} factor R all with Pukanszky 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 II_{1} 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 R equiped with the d_{\infty,2}-metric.
A result is also given showing that the Puk\'anszky invariant is d_{\infty,2}-upper semi-continuous. As a consequence, the sets of masas with Puk\'anszky invariant \{n\} are all closed.

### Publication Details

*Coauthors:* Allan Sinclair

J. London Math. Soc. (2) 75 (2007) 243-254. DOI: 10.1112/jlms/jdl019

*Download:* Journal Website, arXiv.math:0602155, Glasgow ePrint 4610.

Minor typos were corrected at the page proof stage of the published version. The arXiv and on the Glasgow ePrint service contain the version accepted by JLMS and do not correct these typos.

## Boulder Canyon Creek

Why not install a bridge? Colarado, May 2007.