A rotational approach to triple point obstructions

Snyder, Noah

doi:10.2140/apde.2013.6.1923

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A rotational approach to triple point obstructions

Noah Snyder

Vol. 6 (2013), No. 8, 1923–1928

DOI: 10.2140/apde.2013.6.1923

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

Vol. 6, No. 8, 2013