Vol. 6, No. 8, 2013

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
A rotational approach to triple point obstructions

Noah Snyder

Vol. 6 (2013), No. 8, 1923–1928
Abstract

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.

Keywords
subfactors, planar algebras, connections
Mathematical Subject Classification 2010
Primary: 46L37
Milestones
Received: 3 October 2012
Revised: 22 January 2013
Accepted: 8 March 2013
Published: 20 April 2014
Authors
Noah Snyder
Mathematics Department
Indiana University
831 E. Third St.
Bloomington, IN 47401
United States