A rotational approach to triple point obstructions

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

Noah Snyder

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors