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

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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.

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Authors and Affiliations

  1. Mathematics Department, University of California, Berkeley, CA, 94720, USA

    Scott Morrison

  2. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Noah Snyder

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  1. Scott Morrison
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  2. Noah Snyder
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Correspondence to Scott Morrison.

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Communicated by Y. Kawahigashi

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

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Morrison, S., Snyder, N. Subfactors of Index less than 5, Part 1: The Principal Graph Odometer. Commun. Math. Phys. 312, 1–35 (2012). https://doi.org/10.1007/s00220-012-1426-y

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