, Volume 312, Issue 1, pp 1-35
Date: 22 Feb 2012

Subfactors of Index less than 5, Part 1: The Principal Graph Odometer

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Abstract

In this series of papers we show that there are exactly ten subfactors, other than A subfactors, of index between 4 and 5. Previously this classification was known up to index \({3+\sqrt{3}}\) . In the first paper we give an analogue of Haagerup’s initial classification of subfactors of index less than \({3+\sqrt{3}}\) , showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.

Communicated by Y. Kawahigashi
Copyright © 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.