## A rotational approach to triple point obstructions.(English)Zbl 1297.46044

Summary: Subfactors where the initial branching point of the principal graph is $$3$$-valent are subject to strong constraints called triple point obstructions. Since more complicated initial branches increase the index of the subfactor, triple point obstructions play a key role in the classification of small index subfactors. There are two strong triple point obstructions, called the triple-single obstruction and the quadratic tangles obstruction. Although these obstructions are very closely related, neither is strictly stronger. In this paper we give a more general triple point obstruction which subsumes both. The techniques are a mix of planar algebraic and connection-theoretic techniques with the key role played by the rotation operator.

### MSC:

 46L37 Subfactors and their classification

### Keywords:

subfactors; planar algebras; connections
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