Subfactors of index less than 5, part 1: the principal graph odometer

Details Subfactors of index less than 5, part 1: the principal graph odometer Subfactors of index less than 5, part 1: the principal graph odometer

2010-07-10

arxiv.org/abs/1007.1730v2

Mathematics

Operator Algebras

36 pages (updated to reflect that the classification is now complete)

Scientific paper

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ 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.

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