Communications in Mathematical Physics

, Volume 312, Issue 1, pp 1–35 | Cite as

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

  • Scott MorrisonEmail author
  • Noah Snyder


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.


Triple Point Fusion Category Graph Norm Root Vertex Quadruple Point 
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© The Author(s) 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsColumbia UniversityNew YorkUSA

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