Subfactors of index less than 5, Part 1: The principal graph odometer

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 +√3. In the first paper we give an analogue of Haagerup’s initial classification of subfactors of index less than 3 +√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. Show more